Solve the system by substitution. SHOW WORK -X - Y - Z=-8 - 4X +4Y +5Z=7 2X + 2Z=4

1 answer:

3 0

Solve:

<span>-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.

</span>-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!!

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