Question 931143
<pre>
Here's one exactly like it.  Use it as a guide.
Do the same things all the way through.  Just
use your numbers instead:

7x - 8y = -21
 x -  y = -2

<pre><font size = 4><b>
Write the system as:

{{{7x - 8y = -21}}}
{{{1x - 1y =  -2}}}

Then write that as:

{{{ 
( matrix(2,2,7,-8,1,-1) )
( matrix(2,1,x,y) ) = ( matrix(2,1,-21,-2) ) }}}

Now we must find the inverse of the 2x2 
coefficient matrix {{{( matrix(2,2,7,-8,1,-1) )}}}

To find the inverse matrix of a 2x2 matrix:

{{{( matrix(2,2,7,-8,1,-1) )}}}

1.  Find the value of its determinant:

{{{abs( matrix(2,2,7,-8,1,-1)) = (7)(-1)-(-8)(1) = -7+8 = 1}}}

2.  Swap the upper left and lower right elements of {{{( matrix(2,2,7,-8,1,-1) )}}}:

{{{( matrix(2,2,-1,-8,1,7) )}}}

3. Change the sign of the upper right and lower left elements.

{{{( matrix(2,2,-1,8,-1,7) )}}}

4. Divide every element by the value of the determinant found
   in step 1.

{{{( matrix(2,2,(-1)/1,8/1,(-1)/1,7/1) )}}}

{{{( matrix(2,2,-1,8,-1,7) )}}}

-----------------

Next we left-multiply both sides of the equation

{{{ 
( matrix(2,2,7,-8,1,-1) )
( matrix(2,1,x,y) ) = ( matrix(2,1,-21,-2) ) }}}

by the inverse {{{( matrix(2,2,-1,8,-1,7) )}}}

and we get:

{{{ 
( matrix(2,2,-1,8,-1,7) )( matrix(2,2,7,-8,1,-1) )
( matrix(2,1,x,y) ) = ( matrix(2,2,-1,8,-1,7) )( matrix(2,1,-21,-2) ) }}} 

Next we multiply the first two matrices on the left:

{{{ 
( matrix(2,2,(-1)(7)+(8
)(1),(-1)(-8)+(8)(-1),(-1)(7)+(7)(1),(-1)(-8)+(7)(-1)) )( matrix(2,1,x,y) ) = ( matrix(2,2,-1,8,-1,7) )( matrix(2,1,-21,-2) ) }}} 

Simplifying,

{{{ 
( matrix(2,2,-7+8,8-8,-7+7,8-7) )( matrix(2,1,x,y) ) = ( matrix(2,2,-1,8,-1,7) )( matrix(2,1,-21,-2) ) }}}

{{{ 
( matrix(2,2,1,0,0,1) )( matrix(2,1,x,y) ) = ( matrix(2,2,-1,8,-1,7) )( matrix(2,1,-21,-2) ) }}}

Now multiply the two matrices on the left:

{{{ 
( matrix(2,1,1x+0y,0x+1y) ) = ( matrix(2,2,-1,8,-1,7) )( matrix(2,1,-21,-2) ) }}}

Simplifying:

{{{ 
( matrix(2,1,x,y) ) = ( matrix(2,2,-1,8,-1,7) )( matrix(2,1,-21,-2) ) }}}

Now multiply the two matrices on the right:

{{{ 
( matrix(2,1,x,y) ) = ( matrix(2,1,(-1)(-21)+(8)(-2),(-1)(-21)+(7)(-2) ) )}}}

Simplifying

{{{ 
( matrix(2,1,x,y) ) = (  matrix(2,1,21-16,21-14 ))   }}}

{{{ 
( matrix(2,1,x,y) ) = (  matrix(2,1,5,7 ))   }}}

So the solution is;  {{{x=5}}},{{{y=7}}}

Edwin</pre>