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

1 Answer
Feb 14, 2017

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

Explanation:

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))