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------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/master06.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/preview.wmf Content-Transfer-Encoding: base64 Content-Type: image/x-wmf AQAJAAAD4gAAAAYAMAAAAAAABAAAAAMBCAAFAAAACwIAAAAABQAAAAwCeQChAAMAAAAeAAcAAAD8 AgAA////AAAABAAAAC0BAAAIAAAA+gIFAAAAAAD///8ABAAAAC0BAQAOAAAAJAMFAP///////3gA oAB4AKAA////////CAAAAPoCAAAAAAAAAAAAAAQAAAAtAQIABwAAAPwCAAD///8AAAAEAAAALQED AAQAAAAnAf//HAAAAPsC+f8AAAAAAACQAQAAAAAAQAAiQXJpYWwAAAAAAAAAAAAAAAAAAAAAAAAA AAAAAAAAAAAEAAAALQEEAAQAAAAuARgABAAAAAIBAQAFAAAACQIAAAACMAAAADIKCAAnABsAAABT eXN0ZW1zIG9mIExpbmVhciBFcXVhdGlvbnMABQADAAQAAgAEAAYABAACAAQAAgACAAQAAgAEAAMA BAACAAIABQAEAAQABAACAAIABAADAAMABAAAAC4BAAAcAAAA+wIQAAcAAAAAALwCAAAAAAECAiJT eXN0ZW0AAAAAAAAAAAAAGAAAAAIAAACo3RMC5AQAAAQAAAAtAQUABAAAAPABBAADAAAAAAA= ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/pres.xml Content-Transfer-Encoding: quoted-printable Content-Type: text/xml; charset="utf-8" ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0011.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0111.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity.
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0112.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, <= /span>
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0113.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $.
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0114.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $. If there are two unknowns, we need two pieces = of information to solve them,
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0115.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $. If there are two unknowns, we need two pieces = of information to solve them, three unknowns needs three piec= es of information, etc…
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0116.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $. If there are two unknowns, we need two pieces = of information to solve them, three unknowns needs three piec= es of information, etc… These lead to systems of equations.<= /span>
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0117.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $. If there are two unknowns, we need two pieces = of information to solve them, three unknowns needs three piec= es of information, etc… These lead to systems of equations.<= /span>
A system of linear equations is a collection two or more linear = = equations= in two or more variables.
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0118.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $. If there are two unknowns, we need two pieces = of information to solve them, three unknowns needs three piec= es of information, etc… These lead to systems of equations.<= /span>
A system of linear equations is a collection two or more linear = equations= in two or more variables.
A solution<= /i> for the = system is a collection of numbers, one for each variable, that wo= rks for all equations in the system.
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0119.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $. If there are two unknowns, we need two pieces = of information to solve them, three unknowns needs three piec= es of information, etc… These lead to systems of equations.<= /span>
A system of linear equations is a collection two or more linear = equations= in two or more variables.
A solution<= /i> for the = system is a collection of numbers, one for each variable, that wo= rks for all equations in the system.
For example,
<= /div>
 2x + y =3D 7     
   x + y =3D 5       = 3;
<= /div>
is a system.
{
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0120.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $. If there are two unknowns, we need two pieces = of information to solve them, three unknowns needs three piec= es of information, etc… These lead to systems of equations.<= /span>
A system of linear equations is a collection two or more linear = equations= in two or more variables.
A solution<= /i> for the = system is a collection of numbers, one for each variable, that wo= rks for all equations in the system.
For example,
<= /div>
 2x + y =3D 7     
   x + y =3D 5       = 3;
<= /div>
is a system. x =3D 2 and y =3D = 3 is a solution because it fits both equations the ordered pair.
{
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0121.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
In general, we need one piece of information to solve for one unknown quantity. If 2 hamburgers cost 4 dollars and x is the cost of a hamburger, t= hen 2x =3D 4 or x =3D 2 $. If there are two unknowns, we need two pieces = of information to solve them, three unknowns needs three piec= es of information, etc… These lead to systems of equations.<= /span>
A system of linear equations is a collection two or more linear = equations= in two or more variables.
A solution<= /i> for the = system is a collection of numbers, one for each variable, that wo= rks for all equations in the system.
For example,
<= /div>
 2x + y =3D 7     
   x + y =3D 5       = 3;
<= /div>
is a system. x =3D 2 and y =3D = 3 is a solution because it fits both equations the ordered pair. This solution= is written as (2, 3).
{
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0081.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
=
=
Example A.=
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0122.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
=
=
Example A.=
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0123.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  
{
=
=
Example A.=
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0124.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
Example A.=
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0135.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
Example A.=
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0135_image001.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0135_image002.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0125.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:#006600;mso-fareast-language:ZH-CN'>difference between the cost is $2,
=
=
Example A.=
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0125_image003.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0125_image004.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0126.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the difference between the cost is $2, so the hamburger is $2. 
=
=
Example A.=
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0126_image005.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0126_image006.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0127.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the difference between the cost is $2, so the hamburger is $2. 
In symbols, subtr= act the equations, i.e. E1 – E2:
=
=
Example A.=
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0127_image007.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0127_image008.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0128.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the difference between the cost is $2, so the hamburger is $2. 
In symbols, subtr= act the equations, i.e. E1 – E2:
=
=
Example A.=
   2x + <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>y =3D 7 = ;
)    x + y =3D 5    
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0128_image009.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAACQ AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3rAAADs= ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0128_image010.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAIAgAAAAP8AAAIFjI+pywUAOw== ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0128_image011.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0128_image012.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0129.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the difference between the cost is $2, so the hamburger is $2. 
In symbols, subtr= act the equations, i.e. E1 – E2:
=
=
Example A.=
   2x + <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>y =3D 7 = ;
)    x + y =3D 5    
    x + 0 =3D 2<= /span>
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0129_image013.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAACQ AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3rAAADs= ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0129_image014.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAIAgAAAAP8AAAIFjI+pywUAOw== ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0129_image015.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0129_image016.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0130.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the difference between the cost is $2, so the hamburger is $2. 
In symbols, subtr= act the equations, i.e. E1 – E2:
=
=
Example A.=
   2x + <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>y =3D 7 = ;
)    x + y =3D 5    
    x + 0 =3D 2&= #13;
so      x =3D 2
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0130_image017.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAACQ AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3rAAADs= ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0130_image018.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAIAgAAAAP8AAAIFjI+pywUAOw== ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0130_image019.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0130_image020.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0131.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the difference between the cost is $2, so the hamburger is $2. 
In symbols, subtr= act the equations, i.e. E1 – E2:
=
=
Example A.=
Substitute 2 for x back into E2,
we get:     2 + y =3D 5<= /span>
   2x + <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>y =3D 7 = ;
)    x + y =3D 5    
    x + 0 =3D 2&= #13;
so      x =3D 2
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0131_image021.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAACQ AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3rAAADs= ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0131_image022.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAIAgAAAAP8AAAIFjI+pywUAOw== ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0131_image023.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0131_image024.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0132.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the difference between the cost is $2, so the hamburger is $2. 
In symbols, subtr= act the equations, i.e. E1 – E2:
=
=
Example A.=
Substitute 2 for x back into E2,
we get:     2 + y =3D 5&= #13;
        = ;        or    y =3D = 3
   2x + <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>y =3D 7 = ;
)    x + y =3D 5    
    x + 0 =3D 2&= #13;
so      x =3D 2
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0132_image025.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAACQ AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3rAAADs= ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0132_image026.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAIAgAAAAP8AAAIFjI+pywUAOw== ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0132_image027.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0132_image028.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0133.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose two hamburgers and a fry cost $7, and one
hamburger and one= fry cost $5.
Let x =3D cost of a hamburger,  y =3D cost of a fry.
We can translate these into the system:
2x + y =3D 7 =
  x + = y =3D 5    
{
=
=
The differe= nce between the order is one hamburger and the difference between the cost is $2, so the hamburger is $2. 
In symbols, subtr= act the equations, i.e. E1 – E2:
=
=
Example A.=
Substitute 2 for x back into E2,
we get:     2 + y =3D 5&= #13;
        = ;        or    y =3D = 3
Hence the solutio= n is (2 , 3) or,
$2 for a hamburge= r, $3 for a fry.        = ;  
   2x + <= span lang=3DEN-US style=3D'mso-fareast-font-family:\5B8B\4F53;mso-hansi-font-fa= mily: Arial;font-size:133%;color:red;mso-fareast-language:ZH-CN'>y =3D 7 = ;
)    x + y =3D 5    
    x + 0 =3D 2&= #13;
so      x =3D 2
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0133_image029.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhkwADAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAIAAACQ AAIAgAAAAAAAAAIPjI+py+0Po5y02ouz3rAAADs= ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0133_image030.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhFAAEAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAS AAIAgAAAAP8AAAIFjI+pywUAOw== ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0133_image031.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0133_image032.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0110.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
=
=
Example B.=
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0136.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
=
=
Example B.=
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0137.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0138.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D= 18
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
E1    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0138_image033.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0139.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0139_image034.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0139_image035.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0140.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0140_image036.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0140_image037.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0141.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
We have to adjust the equations before we add or subtract = them to eliminate one of the variable.
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0141_image038.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0141_image039.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0142.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
We have to adjust the equations before we add or subtract = them to eliminate one of the variable.
Suppose we chose to eliminate the y-terms, we find the LCM <= /span>= of 3y and 2y first.
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0142_image040.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0142_image041.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0143.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
We have to adjust the equations before we add or subtract = them to eliminate one of the variable.
Suppose we chose to eliminate the y-terms, we find the LCM <= /span>= of 3y and 2y first. It's 6y.
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0143_image042.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0143_image043.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0144.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
We have to adjust the equations before we add or subtract = them to eliminate one of the variable.
Suppose we chose to eliminate the y-terms, we find the LCM <= /span>= of 3y and 2y first. It's 6y. Then we multiply E1 by 2,
E1    
E2    
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0144_image044.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0144_image045.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0145.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
We have to adjust the equations before we add or subtract = them to eliminate one of the variable.
Suppose we chose to eliminate the y-terms, we find the LCM <= /span>= of 3y and 2y first. It's 6y. Then we multiply E1 by 2,
E1    
E2    
8x + 6y =3D 36   
E1*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>2:
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0145_image046.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0145_image047.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0146.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
We have to adjust the equations before we add or subtract = them to eliminate one of the variable.
Suppose we chose to eliminate the y-terms, we find the LCM <= /span>of 3y and 2y first. It's 6y. Then we multiply E1 by 2, E2 by (-3),
E1    
E2    
8x + 6y =3D 36   
-9x –= 6y =3D -39    <= /div>
E1*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>2:
E2*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>(-3):
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0146_image048.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0146_image049.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0147.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
We have to adjust the equations before we add or subtract = them to eliminate one of the variable.
Suppose we chose to eliminate the y-terms, we find the LCM <= /span>of 3y and 2y first. It's 6y. Then we multiply E1 by 2, E2 by (-3), = and add the results, the y-terms are eliminated.
E1    
E2    
8x + 6y =3D 36   
-9x –= 6y =3D -39    <= /div>
E1*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>2:
E2*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>(-3):
+ )=
Systems of Linear Equations
------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0147_image050.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0147_image051.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhKgACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAQAn AAEAgAAAAAAAAAIKjAN5qJewXmymAAA7 ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0147_image052.gif Content-Transfer-Encoding: base64 Content-Type: image/gif R0lGODlhngACAHcAMSH+GlNvZnR3YXJlOiBNaWNyb3NvZnQgT2ZmaWNlACH5BAEAAAAALAEAAACc AAEAgAAAAAAAAAILjI+py+0Po5y0ngIAOw== ------=_NextPart_01C8FAF7.624A6D10 Content-Location: file:///C:/D928D0D1/3SystemofLinearEquations1_files/slide0148.htm Content-Transfer-Encoding: quoted-printable Content-Type: text/html; charset="us-ascii" System of Linear Equations
4x + 3y =3D 18 &#= 13;
3x + 2y =3D 13   
Suppose four hamburgers and three fry cost $18, and three
hamburger and two= fry cost $13. How much does each cost?
Let x =3D cost of a hamburger,  y =3D cost of a f= ry.
We translate these into the system:
=
=
Example B.=
{
Subtracting= the equations now will not eliminate the x nor y.
We have to adjust the equations before we add or subtract = them to eliminate one of the variable.
Suppose we chose to eliminate the y-terms, we find the LCM <= /span>of 3y and 2y first. It's 6y. Then we multiply E1 by 2, E2 by (-3), = and add the results, the y-terms are eliminated.
E1    
E2    
8x + 6y =3D 36   
-9x –= 6y =3D -39    <= /div>
E1*<= span lang=3DEN-US style=3D'font-size:133%;color:#006600;mso-fareast-language:ZH= -CN'>2: