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

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

Explanation:

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