Precalculus, Chapter 8, 8.1, Section 8.1, Problem 78

Given system of equations are ,
x - 3y = 5, -2x + 6y = -10

so the matrix A,B are as follows,
A = 1 -3
-2 6
and B = 5
-10

so the augmented matrix is
[AB] = 1 -3 5
-2 6 -10
step 1 . Divide the 2nd row with -2 we get
1 -3 5
1 -3 5

Both the rows are same
step 2. subtract the the 1st row from second row and restore the 2nd row
1 -3 5
0 0 0
so , now we can say that the value of "y" is any vaule and the value of "x" is dependent on "y".
i.e x = 5+3y
And so x,y are having INFINITE number of solution sets to satisfy the system of equations given.