Precalculus, Chapter 8, 8.1, Section 8.1, Problem 77

Given system of equations are
8x - 4y = 7, 5x + 2y = 1
so the matrices A and B are given as follows
A = [[8, -4], [5, 2]]
B = [[7], [1]]
so the augmented matrix is [AB] = [[8, -4, 7], [5, 2, 1]]
on solving this we get the values of x,y .
step 1 . Make the pivot in the 1st column by dividing the 1st row by 8
[[1, -1/2, 7/8], [5, 2, 1]]

step 2 . muptiply the 1st row by 5
[[5, -5/2, 35/8], [5, 2, 1]]

step 3 . subtract the 1st row from the 2nd row
[[1, -1/2, 7/8], [0, 9/2, -27/8]]

step 4 divide the second row by 9/2
[[1, -1/2, 7/8], [0, 1, -3/4]]

step 5 multiply the 2nd row by -1/2 and subtract the 2nd row from the 1st row
[[1, 0, 1/2], [0, 1, -3/4]]

so, the values of x, y are x= 1/2 and y = -3/4