Question

Solve each system by elimination.

1) -5x - 4y + 6z = -30
4x + 4y + 2z = -4
-3.r - 4y +z = -6
A) (-1, -3,1)
C) (2.-4,-1)
B) (2,-1,-4)
D) (-1. 2.-4)

Answer 1

(2, -1, -4).

Explanation:

-5x - 4y + 6z = -30

4x + 4y + 2z = -4

-3x - 4y +z = -6

Adding the first and second equation eliminates y:

-x + 8z = -34

Adding the second and third equation eliminates y:

x + 3z = -10

Adding theses last 2 equations eliminates x:

11z = -44

z = -4.

Substitute for z in the last equation:

x + 3(-4) = -10

x = -10 + 12 = 2.

Finally substituting for x and z in the first equation in the question:

-5(2) - 4y + 6(-4) = -30

-10 - 4y - 24 = -30

-4y = -30 + 24 + 10 = 4

y = -1.