Question

Solve the three variable system. (I was just introduced to these)

Answer 1

First we have to get down to a system of two equations, then we can work from there. adding the first and third equation together, we get

$x - y + (y - 2z) = 2 + ( - 3) \\ x - 2z = - 1$
now multiply the second equation by 2, and add it to our new equation

$6x + 2z = 22 \\ 6x + 2z + (x - 2z) = 22 - 1 \\ 7x = 21 \\ x = 3$

now plug x into the second equation

3(3) + z = 11

z = 2

and plug it into the first equation

3 - y = 2

y = 1

Answer 2

So basically you do two of the equations first and then solve for the last equation. Please Refer To The Picture