Question

Solve

4x - 2y + z =6
-2x + y = -4
3y - 2z = 4
Answer in the for (x, y, z) in the simplest terms.

Answer 1

(2, 0, - 2 )

Explanation:

4x - 2y + z = 6 → (1)

- 2x + y = - 4 → (2)

3y - 2z = 4 → (3)

multiplying (2) by 2 and adding to (1) will eliminate both x and y

- 4x + 2y = - 8 → (4)

add (1) and (4) term by term to eliminate x and y

0 + 0 + z = - 2

z = - 2

substitute z = - 2 into (3) and solve for y

3y - 2(- 2) = 4

3y + 4 = 4 ( subtract 4 from both sides )

3y = 0 ⇒ y = 0

substitute y = 0 into (2) and solve for x

- 2x + 0 = - 4

- 2x = - 4 ( divide both sides by - 2 )

x = 2

solution is (2, 0, - 2 )