Question

Solve the following system of equations.

4x + 3y + z = -10
x - 3y + 2z = -8
11x - 2y + 3z = -38

Answer 1

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