What is the solution to the system?

5x-y+z=4

x+2y-z=5

2x+3y-3z=5

Eliminate one variable at a time. We have three equations so we can solve for three variables.

(5x-y+z=4) - 5 (x+2y-z=5) = - 11y+6z=-21

-2 (x+2y-z=5) + (2x+3y-3z=5) = - y-z=-5

Now using the two yz equations above to cancel out z

(-11y+6z=-21) + 6 (-y-z=-5) = - 17y=-51

-17y=-51 divide both sides by - 17

y=3, making - y-z=-5 become:

-3-z=-5, z=2, making 5x-y+z=4 become:

5x-3+2=4

5x-1=4

5x=5

x=1

So the solution to the system of equations, (x, y, z) is (1,3,2)