You have:

x_1 + 3x_3 = 20

x_2 + 2x_3 = -2

x_3 = 4;

You can check yourself to see if this works.

20 + 4(3) = 24? No.

Get the matrix in row reduced echelon form. First, -2*Row 3 + Row 2

= Matrix([[1, 0, 3, 20],[0, 1, 0, -10],[0, 0, 1, 4]]

-3*Row 3 + Row 1

= Matrix([[1, 0, 0, 8],[0, 1, 0, -10],[0, 0, 1, 4]]

Now:

x_1 = 8

x_2 = -10

x_3 = 4

8 + 3(4) = 20? Yes.

-10 + 2(4) = -2? Yes.

x_3 = 4? Yes.