How do you solve $4 x + 5 y = - 7$ $4x + 5y = -7$ and $3 x - 6 y = 24$ $3x - 6y = 24$ using matrices?

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Answer 1 · 2017-03-09T06:54:38

The solution is $((x),(y))=((2),(-3))$

We rewrite the equatins in matrix form

$((4,5),(3,-6))((x),(y))=((-7),(24))$

Let $A=((4,5),(3,-6))$

We need the inverse of matrix $A$

First, we calculate the determinant of matrix $A$

$detA=|(4,5),(3,-6)|=-24-15=-39$

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

$A^-1=-1/39((-6,-5),(-3,4))$

$=((6/39,5/39),(3/39,-4/39))$

Therefore,

$((x),(y))=((6/39,5/39),(3/39,-4/39))((-7),(24))$

$=((-42/39+120/39),(-21/39-96/39))$

$=((78/39),(-117/39))$

$=((2),(-3))$

How do you solve 4x + 5y = -7 4x+5y=−74x + 5y = -7 and 3x - 6y = 243x−6y=243x - 6y = 24 using matrices?