Question 632358
  <pre><font face = "Tohoma" size = 3 color = "indigo"><b> 
Hi,
Solve the system of equations by using the inverse of the coefficient matrix.
 x+5y = 25 
5x+5y = 45
{{{A = (matrix(2,2,a1,b1,a2,b2)) = a1b2-b1a2}}}                                  
{{{A =( matrix(2,2,1,5,5,5))}}} = -20
{{{A^(-1) = (1/(a1b2 - b1a2))(matrix(2,2,b2,-b1,-a2,a1))}}}
{{{A^(-1) = (-1/20)(matrix(2,2,5,-5,-5,1))= (matrix(2,2,-.25,.25,.25,-.05)) }}}

and...
{{{(matrix(2,1,x,y))= (matrix(2,2,-.25,.25,.25,-.05))(matrix(2,1,25,45))= (matrix(2,1,5,4)) }}}

Checking our answer using the Elimination Method:
 x+5y = 25 
5x+5y = 45   |Subtracting 1st EQ from the 2nd
  4x = 20  
   x = 5  and y = 4  as {{{5+5*4 = 25}}}
(x,y) Ordered pair (5,4) the solution for this system of equations