Question

Using complete sentences, explain which method you would use to solve the following system of equations and why. In your answer, include the solution to one of the variables and how you found it using the method you chose.

x - 5y + 2z = 0
x + 4y - z = 12
2x - y + 3z = 10

Answer 1

I would use the elimination method because there is 3 variables
x - 5y + 2z = 0 -->(-1)x - 5y + 2z = 0
x + 4y - z = 12
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-x + 5y - 2z = 0 (result of multiplying by -1)
x + 4y - z = 12
--------------add
0 + 9y - 3z = 12
9y - 3z = 12

x + 4y - z = 12 -->(-2)x + 4y - z = 12
2x - y + 3z = 10
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-2x - 8y + 2z = -24 (result of multiplying by -2)
2x - y + 3z = 10
--------------add
0 - 9y + 5z = - 14
-9y + 5z = - 14

9y - 3z = 12
-9y + 5z = - 14
---------------add
0 + 2z = - 2
2z = - 2
z = -1

9y - 3z = 12
9y - 3(-1) = 12
9y + 3 = 12
9y = 12 - 3
9y = 9
y = 1

x - 5y + 2z = 0
x - 5(1) + 2(-1) = 0
x - 5 - 2 = 0
x - 7 = 0
x = 7

check...
x + 4y - z = 12
7 + 4(1) -(-1) = 12
7 + 4 + 1 = 12
12 = 12 (correct)

ANSWER : x = 7, y = 1, z = -1