Solve the system by elimination.

-2x+2y+3z=0

-2x-y+z=-3

2x+3y+3z=5

-2x + 2y + 3z = 0 → 2x - 2y - 3z = 0 → 2x - 2y - 3z = 0

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

2x + 3y + 3z = 5 → 2x + 3y + 3z = 5 - 3y - 2z = - 3

-2x + 2y + 3z = 0 → 2x - 2y - 3z = 0

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

2x + 3y + 3z = 5 → 2x + 3y + 3z = 5 → 2x + 3y + 3z = 5

-2y - 4z = - 2

-3y - 2z = - 3 → - 6y - 4z = - 6

-2y - 4z = - 2 → - 2y - 4z = - 2

-4y = - 4

-4 - 4

y = 1

-3y - 2z = - 3

-3 (1) - 2z = - 3

-3 - 2z = - 3

+ 3 + 3

-2z = 0

-2 - 2

z = 0

-2x + 2y + 3z = 0

-2x + 2 (1) + 3 (0) = 0

-2x + 2 + 0 = 0

-2x + 2 = 0

- 2 - 2

-2x = - 2

-2 - 2

x = 1

(x, y, z) = (1, 1, 0)