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))#