Solve the following system of equations.

4x + 3y + z = - 10

x - 3y + 2z = - 8

11x - 2y + 3z = - 38

That's a 3x3 linear system. Let's do Gaussian elimination

4 3 1 - 10 A

1 - 3 2 - 8 B

11 - 2 3 - 38 C

0 15 - 7 22 D=A-4B

0 31 - 19 50 E=C-11B

0 1 - 7/15 22/15 F=D/15

1 0 3/5 - 18/5 G=B+3F

0 0 - 68/15 68/15 H=E-31F - 19-31 (-7/15), 50-31 (22/15)

0 0 1 - 1 I=-15/68 H

1 0 0 - 3 J=G - 3/5 I

0 1 0 1 K=F + 7/15 I

We read off from the last three lines the

Answer: x=-3, y=1, z=-1