Question

Solve the system using elimination?
-2x+2y+3z=0,
-2x-y+z=-3,
2x+3y+3z=5

Answer 1

well looking at the equations, which letter do you think you should eliminate 1st..?

Answer 2

x?

Answer 3

Answer is x = 1, y = 1 and z = 0.

Answer 4

so add equations 1 and 3, this will eliminate x

-2x + 2y + 3x = 0
2x + 3y + 3z = 5
-----------------\
5y + 6z =5 equation 4



same for equation 2 and 3

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

divide each term by 2 and you get

y + 2z = 1 equation 5

so you now need to solve

5y + 6z = 5
y + 2z = 1

so multiply equation 5 by -3 and add to equation 4

5y + 6z = 5
-3y - 6z = -3
----------------
2y = 2

solve for y. Find z by substituting into equations 4 or 5

then when you gte that you can find x by substituting your y and z values into any of the initial equations.

hope it helps