Solve the following system of equations for all three variables.

Question

2x+6y+z=-6

6x-5y-z=-2

4x+4y+z=-8

Answer 1

This is a fairly simple set to solve.

First add equation 2 to equation 1 and equation 3.

This will eliminate z.

Then add the resultant 2 equations, which will eliminate z.

Then you will find x=-1.

Then go back and get y and z from the equations above.

Answer 2

I suggest you solve using Cramer's rule. It is very tedious to type all of that in, but here are some intermediate results and the final answer, so you can check your work:

Principal determinant: D = -18

x determinant: D_x = 18

y determinant: D_y = 0

z determinant: D_z = 72

Answer:

x = D_x/D = -1

y = D_y/D = 0

z = D_z/D = -4

Test the answer. These 3 values satisfy the given equations.