Use the elimination method to solve the following system of equations.

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

The answer 
2x - y + z = -3          (1)
2x + 2y + 3z = 2       (2)
3x - 3y - z = -4          (3)

 (1) - (2)              3y +2z =5
 3 .(1) - 2.(2)       3y+5z = -1

let 's solve 
3y +2z =5
3y+5z = -1
z= - 2, and 3y =5+4=9,  y=3, so  2x - 3 -2 = -3 implies x= 1

finally x=1, y=3 and z= -2
proof 
2x - y + z = -3??     2.1 - 3 -2 = -3  (true)