How do I find x, y, and z in the following system?

Question

2x + 3y - z = 17
3x - y + 2z = 11
x - 3y + 3z = -4

Answer 1

using substitution,
z = 2x+3y-17, so
3x-y+2(2x+3y-17) = 11
x-3y+3(2x+3y-17) = -4
that leaves
7x+5y = 45
7x+6y = 47
subtract and you get
y = 2
so 7x=35, making x=5
z = 2*5+3*2-17 = -1

I guess you could also use matrices or determinants, but that's beyond the scope of this post ...