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How do you solve -x-y-3z=-9 z=3x-1 x-5y+z=21 using elimination

How do you solve -x-y-3z=-9 z=3x-1 x-5y+z=21 using elimination-example-1

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Assuming these are three separate problems, I have solved them for you below.

1.)
-x - y - 3z = -9


⇒ -x + (-y + y) + (-3z + 3z) = -9 + 3z + y


⇒ -x = -9 + 3z + y

Multiply the whole thing by -1 so x is positive.


x = 9 - 3z - y

2.)
z = -3x - 1


z + 1 = -3x + (-1 + 1)


z + 1 = -3x

Isolate x⇒
(z + 1 = -3x)/(-3)


(1)/(3)z + (1)/(3) = x

3.)
x - 5y + z = 21


(-x + x) + -5y + (z - z) = 21 - z - x


(-5y = 21 - z - x)/(-5)


y = (1)/(5)x + (1)/(5)z -  (21)/(5)

User Rafal Spacjer
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