Question

Use the substitution method to solve the following system of equations.

3x + y - z = 2
2x + y + 2z = 8
2x - 3y + z = 21

A. (3, 4, 3)
B. (-3, 4, 3)
C. (3, -4, 3)
D. (3, 4, -3)

Answer 1

@texaschic101

Answer 2

C is the solution. Do you understand why?

Answer 3

3x + y - z = 2
2x - 3y + z = 21

5x - 2y = 23

3x + y - z = 2
2x + y + 2z = 8

3x - 2x + y - y - z - 2z = 2 - 8
x - 3z = -6

2x - 2x + y + 3y + 2z - z = 8 - 21
4y + z = -13

z = -13 - 4y
x = -6 + 3z = -6 + 3 * (-13 - 4y) = -6 - 39 - 12y = -45 - 12y

3x + y - z = 2
3 * (-45 - 12y) + y - (-13 - 4y) = 2
-135 - 36y + y + 13 + 4y = 2
5y - 36y - 122 = 2
-31y = 124
y = -4

z = -13 - 4y
z = -13 + 16
z = 3

x = -6 + 3z
x = -6 + 9
x = 3

(3 , -4 , 3)

Answer 4

so yes its C