Question

Solve the following system of equations?

x + 3y - z = 2
x - 2y + 3z = 7
x + 2y - 5z = -21
a)(2, 3, 5)
b)(-2, 3, 5)
c)(2, -3, 5)
d)(2, -3, 5)

Answer 1

1x + 3y - 1z = 2 ⇒ 1x + 3y - 1z = 2
1x - 2y + 3z = 7 ⇒ 1x - 2y + 3z = 7
1x + 2y - 5z = -21 5y - 4z = -5
5y - 4z = -5 ⇒ -20y + 16z = 20
1x + 3y - 1z = 2 -4y + 8z = -28 ⇒ -20y - 40z = -140 1x - 2y + 3z = 7 ⇒ 1x - 2y + 3z = 7 -24z = -120
1x + 2y - 5z = -21 ⇒ 1x + 2y - 5z = -21 -24 -24
-4y + 8z = -28 z = 5
5y - 4(5) = -5
5y - 20 = -5
+20 +20
5y = 15
5 5
y = 3
x + 3(3) - 5 = 2
x + 9 - 5 = 2
x + 4 = 2
-4 -4
x = -2
(x, y, z) = (-2, 3, 5)
The solution to the answer is B. (-2, 3, 5).