Question

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

Answer 1

Answer: -1, 0,-3

Explanation:

Answer 2

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.