3x + 4y -z = 1
3x-y-4z=-3
x+3y-3z = 9

*Use Elimination to solve*

x = -3
y = 2
z = -2

Step-by-step explanation:

When solving by elimination:
• Subtract equations that have a variable with the same coefficient
• Add equations that have a variable with the same coefficient but different sign

1. Label your equations
3x + 4y - z = 1 [1]
3x - y - 4z = -3 [2]
x + 3y - 3z = 9 [3]

2. Add/Subtract equations
[1] - [2], both have “3x”
3x + 4y - z = 1 [1]
3x - y - 4z = -3 [2]
————————
5y + 3z = 4 [4]

Multiply [3] by 3
=> 3x + 9y - 9z = 27 [5]

[5] - [2], both have “3x”
3x + 9y - 9z = 27 [5]
3x - y - 4z = -3 [2]
—————————-
10y - 5z = 30
2y - z = 6
-z = 6 - 2y
z = 2y - 6 [6]

Substitute [6] into [4]
5y + 3z = 4 [4]
5y + 3(2y - 6) = 4
5y + 6y - 18 = 4
11y - 18 = 4
11y = 22
y = 2 ⭐️

Substitute y = 2 into [6]
z = 2y - 6 [6]
z = 2(2) - 6
z = 4 - 6
z = -2 ⭐️

Substitute y = 2, z = -2 into [3]
x + 3y - 3z = 9 [3]
x + 3(2) - 3(-2) = 9
x + 6 + 6 = 9
x + 12 = 9
x = -3 ⭐️

Therefore, x = -3, y = 2 and z = -2.