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⇒ $\frac{z + 1 = -3x}{-3}$

⇒$\frac{1}{3}z + \frac{1}{3} = x$

3.) $x - 5y + z = 21$

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

⇒ $\frac{-5y = 21 - z - x}{-5}$

⇒ $y = \frac{1}{5}x + \frac{1}{5}z - \frac{21}{5}$