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

x = 1, y = - 2, z = 3.

Step-by-step explanation:

x + 2y + 2z = 3 A

2x - 2y - z = 3 B

x - 2z = - 5 C

If we add equations A and B we eliminate y:

3x + z = 6 E

Multiply E by 2:

6x + 2z = 12 F

Adding C and F we get:

7x = 7

x = 1.

Plug this into equaton C:

1 - 2z = - 5

-2z = - 5 - 1 = - 6

z = 3.

Now plugging x = 1 and z = 3 in equation A:

1 + 2y + 2 (3) = 3

2y = 3 - 1 - 6 = - 4

y = - 2.