Question

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

Answer 1

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)`