Solve the system by elimination. -2x + 2y + 3z = 0 -2x - y + z = -3 2x + 3y + 3z = 5 go step by step, !

Equation 1 plus equation 3 to cancel x, you will get: 5y+6z=5
equation 2 plus equation 3, you will get: 2y+4z=2
Now focus on these two new equation you've just got; Let's eliminate y next. To eliminate y, we first have to make the coefficient the same.
multiple 5y+6z=5 by 2 and multiple 2y+4z=2 by 5, we'll get:
10y+12z=10
10y+20z=10
subtract the second of these two equations from the first, you'll get: -8z=0, therefore z=o
Plug z=0 into either one of these two equations, you'll get y=1
plug z=0, y=1 into any of the original three equations, you will get x=1