Solving this System?

Question

3x+2y-z=-11
2x-3y+4z=11
5x+y-2z=-17

Answer 1

3x+2y-z=-11
-10x-2y+4z=34 (3)*-2
adding
-7x+3z=23 (4)
2x-3y+4z=11 (2)
15x+3y-6z=-51 (3)*3
adding
17x-2z=-40 (5)
(4)*-2 14x-6z=-46
(5) *-3 -51x+6z=120
adding
-37x=74
x=-2
sub14+3z=23
z=3
sub y=-1
solution set{-2,-1,3}

Answer 2

Start by multiplying the first equation by 2 and the second equation by 3. This will get a common term of 6x:

6x + 4y - 2z = -22
6x - 9y + 12z = 33

Now you can subtract these:
13y - 14z = -55

Do the same for #2 and #3 using 5 and 2 to eliminate 10x:
10x - 15y + 20z = 55
10x + 2y - 4z = -34

Subtract:
-17y + 24z = 89

Now you can combine this with your prior result:
13y - 14z = -55 <-- Multiply by 17
-17y + 24z = 89 <-- Multiply by 13

221y - 238z= -935
-221y + 312z = 1157

Now add:
74z = 222

Divide both sides by 74:
z = 3

Now you can plug this back into one of the equations:
-17y + 24z = 89
-17y + 24(3) = 89
-17y + 72 = 89
-17y = 17
y = -1

Finally use these two values to get x:
3x+2y-z=-11
3x + 2(-1) -(3) = -11
3x - 2 - 3 = -11
3x = -6
x = -2

So the answer is:
x = -2
y = -1
z = 3