Question

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

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

(3, 4, 3)
(-3, 4, 3)
(3, -4, 3)
(3, 4, -3)

Answer 1

If we have :
8(3x + y - z = 2)=24x+8y-8z=16
and :
2( 2x + y + 2z = 8) = 4x+4y+8z=16
So can say :
24x+8y-8z=4x+4y+8z
k ?:)

Answer 2

@Futuristicmario

Answer 3

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

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

y = -3x + z + 2
y = -3(3z - 6) + z + 2
y = -9z + 18 + z + 2
y = -8z + 20

2x - 3y + z = 21
2(3z - 6) - 3(-8z + 20) + z = 21
6z - 12 + 24z - 60 + z = 21
31z - 72 = 21
31z = 93
z = 3

x = 3z - 6
x = 3(3) - 6
x = 9 - 6
x = 3

y = -8z + 20
y = - 8(3) + 20
y = -24 + 20
y = - 4

check...
3x + y - z = 2
3(3) +(-4) - 3 = 2
9 - 4 - 3 = 2
9 - 7 = 2
2 = 2 (correct)

check...2x - 3y + z = 21
2(3) - 3(-4) + 3 = 21
6 + 12 + 3 = 21
21 = 21 (correct)

x = 3, y = -4, and z = 3