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,

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

How do you solve 2x+2y = 22x+2y = 2 and 4x+3y=74x+3y=7 using matrices?