How do you solve #2x+2y = 2# and #4x+3y=7# using matrices?

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Answer 1 · 2017-01-28T12:50:01

The answer is #((x),(y))=((4),(-3))#

The equations are

#2x+2y=2#

#4x+3y=7#

In matrix form , we have

#((2,2),(4,3))*((x),(y))=((2),(7))#

Let #A=((2,2),(4,3))#

We must find the inverse matrix #A^-1#

The determinant of matrix #A# is

#detA=|(2,2),(4,3)|=6-8=-2#

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

#A^-1=1/detA*((3,-2)(-4,2))#

#=-1/2((3,-2),(-4,2))=((-3/2,1),(2,-1))#

Verification

#AA^-1=((2,2),(4,3))*((-3/2,1),(2,-1))=((1,0),(0,1))=I#

Therefore,

#((x),(y))=((-3/2,1),(2,-1))((2),(7))=((4),(-3))#