Question

-9x +5y=8
7X - 4Y=0
SOLVE the system of equations using the inverse of the coefficient matrix

Answer 1

Rewriting this in matrix form looks like:
|-9 5||x|=|8|
|7 -4||y|=|0|
multiplying by the inverse of the coefficient matrix on both sides yields (x,y) that solves this system.
There is a simple formula for the inverse of a 2x2 matrix that involves the determinant and shifting and negating some numbers.
If A = |a b|
|c d|
A^(-1) = [1/det(A)] |d -b|
|-c a|

Answer 2

Also, det(A) = ad-bc = -6
So given that info, we can generate
A^(-1) = (-1/6) |-4 -5|
|-7 -9|
and
|x| = (-1/6) |-4 -5| |8| = |(32/6)|
|y| = |-7 -9| |0| |(56/6)|

Answer 3

let me know what doesn't make sense, or if the matrices aren't readable, the equation editor won't work for me =(