Question 1055150
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I corrected here minor deficiencies of the previous solution.
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Inverse matrix of the coefficient matrix is 
{{{A=(matrix(2,2,
2,3,
4,-2))}}}
For a 2x2 system,
{{{B=(matrix(2,2,
a,b,c,d))}}}
the inverse matrix is,
{{{B^(-1)=(1/D)*(matrix(2,2,
d,-b,-c,a))}}}
where the determinant, {{{D}}} = {{{ad-bc)}}}
So then,
{{{D}}} = {{{(2(-2)-4(-3)))}}} = {{{(-4-12)}}} = {{{-16}}}
and
{{{A^(-1)=(-1/16)*(matrix(2,2,-2,-3,-4,2))}}}
{{{A^(-1)=(matrix(2,2,
1/8,3/16,1/4,-1/8))}}}