System of Equations

Question

-x+y+2z=1

2x+3y+z=-2

5x+4y+2z=4

 

I have tried many different ways to solve this and I am completely stuck on how to do these kinds of problems. 

Answer 1

Multiply top equation by 5 and add to bottom equation getting

 

9y + 12z = 9

 

Multiply top equation by 2 and add to middle equation getting

 

5y + 5z = 0, y = -z

 

9(-z) + 12z = 9

-9z + 12z = 9

3z = 9

z = 3

y = -3 

x = 2