Question

Solve the following system of equations and select the correct answer below:

3x + 3y + 2z = −5
x + y + 3z = −4
3x − y + 5z = −8

A. (1, 0, 1)
B. (−1, 0, −1)
C. (1, 0, −1)
D. (−1, 0, 1)

Answer 1

3x + 3y + 2z = -5 ⇒ 3x + 3y + 2z = -5 ⇒ 3x + 3y + 2z = -5
1x + 1y + 3z = -4 ⇒ 1x + 1y + 3z = -4 ⇒ 3x + 3y + 9z = -12
3x - 1y + 5z = -8 -7z = 7
-7 -7
z = -1
3x + 3y + 2z = -5
1x + 1y + 3z = -4 ⇒ 1x + 1y + 3z = -4
3x - 1y + 5z = -8 ⇒ 3x - 1y + 5z = -8
4x + 8z = -12

4x + 8z = -12
4x + 8(-1) = -12
4x - 8 = -12
+ 8 + 8
4x = -4
4 4
x = -1

3x + 3y + 2z = -5
3(-1) + 3y + 2(-1) = -5
-3 + 3y - 2 = -5
3y - 3 - 2 = -5
3y - 5 = -5
+ 5 + 5
3y = 0
3 3
(x, y, z) = (-1, 0, -1)