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

Answer: (-1, 0, - 3)

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