Precalculus, Chapter 8, 8.1, Section 8.1, Problem 71

The augmented matrix is [[-1,1,-22],[3,4,4],[4,-8,32]]
On applying R_1 -gt -R_1 and R_3 -gt (R_3)/4 we get (means inverse the sign of first row and divide the third row by 4)
[[1,-1,22],[3,4,4],[1,-2,8]]
On applying R_2 -gt 3R_1 - R_2 and R_3 -gt R_3 - R_1 we get
[[1,-1,22],[0,-7,62],[0,-1,-14]]
On applying R_3 -gt 7R_3 - R_2 we get
[[1,-1,22],[0,-7,62],[0,0,-160]]
On applying R_2 -gt (R_2)/(-7) we get
[[1,-1,22],[0,1,-62/7],[0,0,-160]]
Hence the given system of equations is equivalent to the following
x - y =22
y = -62/7 and 0(x) + 0(y) =-160
Clearly no x, y satisfy the last equation.
Hence the given system has no solution and is inconsistent