How do you solve the system $3x-5y=-24, 5x+4y=-3$ using matrix equation?

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Answer 1 · 2017-02-14T01:20:19

$((x),(y)) = ((-3),(3))$

$A mathbf x = mathbf b$

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

Here:
$A^(-1) = ((3, -5),(5,4))^(-1) = 1/(3*4 - 5*(-5)) ((4, 5),(-5,3))$

$= 1/(37) ((4, 5),(-5,3))$

So we can say that:

$1/(37) ((4, 5),(-5,3))((3, -5),(5,4))((x),(y)) =1/(37) ((4, 5),(-5,3)) ((-24),(-3))$

$implies ((1, 0),(0,1))((x),(y)) =1/(37) ((4, 5),(-5,3)) ((-24),(-3))$

$implies ((x),(y)) = 1/37 ((-111),(111)) = ((-3),(3))$

How do you solve the system 3x-5y=-24, 5x+4y=-33x-5y=-24, 5x+4y=-3 using matrix equation?