William W. answered • 08/28/20

Math and science made easy - learn from a retired engineer

1) 5x + 2y - 3z = 17

2) 2x + 2y + z = 5

3) 3x + 2y = -6

Use elimination.

First, decide what variable to eliminate first

Since there is no "z" in equation 3), let's eliminate "z" from equations 1) and 2)

Multiply 2) by 3 to get:

2A) 6x + 6y + 3z= 15

Add to 1):

1) 5x + 2y - 3z = 17

2A) 6x + 6y + 3z= 15

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4) 11x + 8y = 32

Using equations 4) and 3) we can now eliminate the "y" by multiplying 3) by -4:

3A) -12x - 8y = 24

And adding to 4):

3A) -12x - 8y = 24

4) 11x + 8y = 32

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5) -x = 56

solving, we get x = -56

Using 3) and plugging in x = -56, we get:

3(-56) + 2y = -6

-168 + 2y = -6

2y = 162

y = 81

Using 2) and plugging in x = -56 and y = 81 we get:

2(-56) + 2(81) + z = 5

-112 + 162 + z = 5

50 + z = 5

z = -45