Solve the system by substitution. show work -x - y - z=-8 - 4x +4y +5z=7 2x + 2z=4

Solve:

-X - Y - Z       =-8
- 4X +4Y +5Z=7
2X + 2Z         =4   is the same as x + z = 2.  Thus, z = 2 - x.

Subst. 2 - x for z in the 1st and second equations.

-X - Y - Z       =-8   becomes -x - y - (2 -x) = -8
- 4X +4Y +5Z=7     becomes -4x + 4y + 5(2-x) = 7

Now we have 2 equations in only 2 unknowns.  Let's simplify them!

-x - y - 2 + x = -8               which becomes   -y = -6, or y = 6
-4x + 4y + 10 - 5x = 7       which becomes   -9x + 4y = 7 - 10 = -3

Now substitute 6 for y in this last equation:  -9x + 4(6) = -3, or
                                                                      -9x + 24 = -3, or
                                                                      -9x = - 27 => x = 3

Then x = 3, y = 6 and z = 2 - x, or z = 2-3, or   z = -1.

The solution is (3, 6, -1).  Check it!!