Solve the following 3 × 3 system. enter the coordinates of the solution below.
2x – 3y – 2z = 4
x + 3y + 2z = –7
–4x – 4y – 2z = 10

The system of equations is
2x -  3y -  2z  = 4                 (1)
   x + 3y + 2z = -7                (2)
-4x - 4y -  2z = 10               (3)

There are many methods for solving the system of equations, including matrix methods. I shall use basic algebraic methods.

Subtract (3) from (1).
6x + y = -6                   (4)
Add (2) and (3).
-3x - y = 3                     (5)
Add (4) and (5).
3x = -3
x = -1
From (4), obtain
y = -6 - 6x
   = -6 +6
   = 0
From (2), obtain
2z = -7 - x - 3y
     = -7 + 1
     = -6
z = -3

(-1, 0, -3)
The solution is x = -1, y = 0, z = -3.