Question

solve the system by elimination: -2x+2y+3z=0 -2x-y+z=-3 2x+3y+3z=5

Answer 1

What kind of help are you looking for?
Have you solved a system of linear equations by elimination before?

In this particular problem, the choice of which variable (x, y or z) to eliminate first is arbitrary (doesn't matter much).

You could use the first and third given equations to eliminate the variable z, and then the first and third to eliminate the variable z again. Then the remaining equations will have only the variables x and y. Sound familiar?

Answer 2

can you show me how to do the work?

Answer 3

Pick 2 equations to work with. I picked these 2:
2x+3y+3z=5
-2x+2y+3z=0

Pick one variable to eliminate by addition or subtraction. I picked x:
(2x+3y+3z=5) + (-2x+2y+3z=0) = 5y+6z=5

Repeat this with the remaining equation. Eliminate the same variable.
(2x+3y+3z=5) + (-2x-y+z=-3) = 2y+4z=2

Eliminate one variable from these equations. I picked z. You may need to multiply the entire equation so they properly eliminate.
2(5y+6z=5) - 3(2y+4z=2) = 4y=4
y=1

Plug the variable you found into one of the shorter 2-variable equations. I used this one:
2y+4z=2
2(1)+4z=2
2+4z=2
4z=0
z=0

Then plug in both variables you found into one of the original equations.
2x+3y+3z=5
2x+3(1)+3(0)=5
2x+3=5
2x=2
x=1

And those should be all of your variables.
x=1 y=1 z=0