Precalculus, Chapter 8, 8.1, Section 8.1, Problem 76

Given system of equations are
5x - 5y = -5, -2x - 3y = 7
so ,we get the matrices as
A = [[5, -5], [-2, -3]]
and
B = [[-5], [7]]
the augmented matrix [AB] = [[5, -5, -5], [-2, -3, 7]]


on solving the [AB] we get the values of x,y
Step 1. Make the pivot in the 1st column by dividing the 1st row by 5
[[1, -1, -1], [-2, -3, 7]]

step 2. Multiply the 1st row by -2
[[-2, 2, 2], [-2, -3, 7]]

step 3. Subtract the 1st row from the 2nd row
[[1, -1, -1], [0, -5, 5]]

step 4. divide the second row with -5 we get
[[1, -1, -1], [0, -1, 1]]

Step 5. subtract the 2 nd row from 1st row we get
[[1, 0, -2], [0, -1, 1]]

step 6. multiply the 2 nd row with -1
[[1, 0, -2], [0, 1, -1]]


so the vlaues of x,y are x= -2 , y =-1