How do you solve the system $9x-6y=12, 4x+6y=-12$ using matrix equation?

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Answer 1 · 2017-02-15T10:21:39

The answer is $((x),(y))=((0),(-2))$

Let's rewrite the equation in matrix form

$((9,-6),(4,6))((x),(y))=((12),(-12))$

Let matrix $A=((9,-6),(4,6))$

We need to calculate $A^-1$ , the inverse of matrix $A$

For a matrix to be invertible,

$detA!=0$

$detA=|(9,-6),(4,6)|=9*6-(-6*4)$

$=54+24=78$

As, $detA!=0$ , the matrix is invertible

$A^-1=1/78((6,6),(-4,9))$

$=((6/78,6/78),(-4/78,9/78))=((1/13,1/13),(-2/39,3/26))$

Therefore,

$((x),(y))=((1/13,1/13),(-2/39,3/26))*((12),(-12))$

$=((0),(-2))$

How do you solve the system 9x-6y=12, 4x+6y=-129x-6y=12, 4x+6y=-12 using matrix equation?