Question

Three Variable Systems of Equations

Find the value of y in the solution to the system of equations.

2x + 2y + 3z = 3

x + 2y + 2z = -1

x - 3y + 5z = 6

Answer 1

2x + 2y + 3z = 3
x + 2y + 2z = -1 -->(-2)
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2x + 2y + 3z = 3
-2x - 4y - 4z = 2 (result of multiplying by -2)
--------------add
-2y - z = 5

x + 2y + 2z = -1 -->(-1)
x - 3y + 5z = 6
---------------
-x - 2y - 2z = 1 (result of multiplying by -1)
x - 3y + 5z = 6
--------------add
-5y + 3z = 7

-2y - z = 5 -->(3)
-5y + 3z = 7
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-6y - 3z = 15 (result of multiplying by 3)
-5y + 3z = 7
------------add
-11y = 22
y = -2

-5y + 3z = 7
-5(-2) + 3z = 7
10 + 3z = 7
3z = 7 - 10
3z = -3
z = -1

2x + 2y + 3z = 3
2x + 2(-2) + 3(-1) = 3
2x - 4 - 3 = 3
2x - 7 = 3
2x = 3 + 7
2x = 10
x = 5

check...
x + 2y + 2z = -1
5 + 2(-2) + 2(-1) = -1
5 - 4 - 2 = -1
5 - 6 = -1
-1 = -1 (correct)

x = 5, y = -2, z = -1

Answer 2

Thanks a bunch!