# Math Help - Need Help With Linear Equations

1. ## Need Help With Linear Equations

To solve a system of three linear equations in three variables by the addition method.

Solve by the addition method:

x + 3y + z = 6
3x + y - z = -2
2x + 2y - z = 1

x - 2y - z = 1
x + 3y + z = 16
3x - y - z = 12

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

3x + 4z = 5
2y + 3z = 2
2x - 5y = 8

the answers should be (?,?,?) can someone help me break it down??!?

2. Originally Posted by sgw89
Solve by the addition method:

x + 3y + z = 6
3x + y - z = -2
2x + 2y - z = 1
Let me help ya with this one.

Add the first and the second equation, so $4x+4y=4\implies x+y=1.$

Add the first and the third equation, so $3x+5y=7.$

From here, you have a $2\times2$ system which you may solve easily.