Question

Solve the following system of equations.

x + 3y + 2z = –16
2x – y + 2z = –15
2x – 2y – z = 1

(–3, –1, –5)

(–3, 5, –2)

(2, –4, –3)

(4, 4, –1)

Answer 1

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Answer 2

x + 3y + 2z = - 16 -->(-2)x + 3y + 2z = - 16
2x - y + 2z = - 15
----------------
-2x - 6y - 4z = 32 (result of multiplying by -2)
2x - y + 2z = - 15
----------------add
-7y - 2z = 17

2x - y + 2z = - 15 -->(-1)2x - y + 2z = - 15
2x - 2y - z = 1
----------------
-2x + y - 2z = 15 (result of multiplying by -1)
2x - 2y - z = 1
----------------add
-y - 3z = 16

-7y - 2z = 17
-y -3z = 16 -->(-7)-y - 3z = 16
--------------
-7y - 2z = 17
7y + 21z = - 112 (result of multiplying by -7)
---------------add
19z = - 95
z = - 5

-y - 3z = 16
-y - 3(-5) = 16
-y + 15 = 16
-y = 16 - 15
-y = 1
y = -1

x + 3y + 2z = - 16
x + 3(-1) + 2(-5) = - 16
x - 3 - 10 = - 16
x - 13 = - 16
x = - 16 + 13
x = - 3

check...
2x - 2y - z = 1
2(-3) - 2(-1) - (-5) = 1
-6 + 2 + 5 = 1
-6 + 7 = 1
1 = 1 (correct)

ANSWER : (-3,-1,-5)