How do you solve a system of equations?

Question

2x – y + z = 8
x + 2y + z = -3
x - 2y – z = 7

Answer 1

The fastest method is to use a graphing calculator and set your system up as a matrix. Solve using Reduced Row Echelon Form (rref) command.

If doing by hand, the answerer above me gave a good method.

Answer 2

2x – y + z = 8
x + 2y + z = -3
x - 2y – z = 7
x - 3y = 11
3x - 3y = 15
2x = 4
x = 2
y = - (11 - 2)/3 = - 3
z = 8 - 4 - 3 = 1

check:
2 + 2(-3) + 1 = - 3

Answer 3

get rid of z in the first and third equation

2x - y + z = 8
x - 2y – z = 7
------------------
3x - 3y = 15

get rid of z in the second and third equation

x + 2y + z = -3
x - 2y – z = 7
-------------------
2x = 4
x = 2

3(2) - 3y = 15
-3y = 9
y = -3

2(2) - (-3) + z = 8
4 + 3 + z = 8
z = 1