SOLUTION: Solve the following system of equations by using reduction. 2x + 2y − 2z = 4 3x + 2y − 2z = −1 − 4y + 5z = 1

Question 1141157: Solve the following system of equations by using reduction.
2x + 2y − 2z = 4
3x + 2y − 2z = −1
− 4y + 5z = 1
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
solve the following system of equations by using reduction.
2x + 2y − 2z = 4
3x + 2y − 2z = −1
− 4y + 5z = 1
:
let m represent(2y-2z)
2x + m = 4
3x + m = -1
--------------subtraction elimnates m, find x
-x = 5
x = -5
:
in the first equation, replace x with -5,
2(-5) + 2y - 2z = 4
2y - 2z = 4 + 10
2y + 2z = 14
multiply equation by 2 and pair with the 3rd equation
4y - 4z = 28
-4y+ 5z = 1
------------addition eliminates y, find z
z = 29
find y using the 3rd equation
-4y + 5(29) = 11
-4y + 145 = 11
-4y = 1 - 145
-4y = -144
y = -144/-4
y = +36
:
We then have x=-5, y = 36, z = 29
:
:
Check solution in the 2nd equation
3x + 2y − 2z = −1
3(-5) + 2(36) - 2(29) =
-15 + 72 - 58 = -1

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