System of equations

Question

Solve the following system of equations for the unknown values of x,y and z. x+2y-z=4;2x+y+z=-2;x+2y+z=2

Answer 1

x + 2y - z = 4 (eq#1)

2x + y + z = -2 (eq.#2)

x + 2y + z = 2 (eq#3)

Add eqs. #1 and #3 together.

x + 2y - z = 4

x + 2y + z = 2

2x + 4y = 6  Divide both sides by 2

x + 2y = 3 (eq.#4)

Multiply eq.#2 by -1 and add to eq.#3

-2x - y - z = 2

x + 2y + z = 2

-x + y = 4 (eq.#5)

Add eqs. #4 and # 5

x + 2y = 3

-x + y = 4

3y = 7

y = 7/3  Substitute into eq.#5

-x + y = 4

-x + 7/3 = 4

-x = 5/3 

x = -5/3 Substitute into eq.#1

-5/3 + 2(7/3) - z = 4

9/3 - z = 4

-z = 1

z = -1

 

(-5/3, 7/3, -1)