Question

Solve the system by elimination
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z

Hey could someone just explain to me how to get started on this question. I can do it I just need help knowing what to do first. Thanks guys

Answer 1

First pick one variable to eliminate. Pick x for instance.
You can eliminate x from the first 2 equations simply by subtracting them.
You can eliminate x from the last 2 equations simply by adding them.
You will be left with two equations with just y and z and no x. You can solve for y and z by further elimination.

Answer 2

You are a saint thanks man

Answer 3

you are welcome. I assume you can take it from here. If not post any further questions below.

Answer 4

The two equations I came up with are 3y+2z=-3 and 2y+5z=2 now I am not sure how to cancel out the next variable. Also I noticed in my post that i forgot to put that 2x+3y+3z=5

Answer 5

Subtracting the first two equations we get:
3y + 2z = +3 ----- (4)
Adding the last two equations we get:
2y + 4z = 2 ----- (5)

You can eliminate z from these two equations by multiplying equation (4) by -2 and adding it to equation (5)
-6y - 4z = -6
2y + 4z = 2

Add them. -4y = -4
Divide both sides by -4
y = 1

Put y = 1 in either equation (4) or (5) and solve for z.

Then put y and z values in one of the first three equations and solve for x.

Answer 6

Awesome thanks again I think I got it now

Answer 7

After solving for x, y and z you cam put those values back in the first three equations to see if it satisfies them. That way you can verify there was no error in the arithmetic when solving for x, y and z.

you are welcome.