Question 1141158
{{{2x + 4y = 5}}}
{{{-x + 3y = -2}}}


Your matrix:


{{{matrix(2,3,2,	4,	5,
-1,	3,	-2)}}}



Write the main matrix:


{{{matrix(2,2,
2,	4,
-1,	3)}}}


{{{D=2*3-4(-1)=6+4=10}}}


Determinant is not zero, therefore inverse matrix exists:


Calculate the inverse matrix


{{{matrix(2,2,3/10,	-2/5,
1/10,	1/5)}}}

Multiply the inverse matrix by the solution vector:


{{{matrix(2,1,23/10,
1/10)}}}


Solution set:


{{{x = 23/10}}}
{{{y = 1/10}}}