Question

Solve the systems by elimination
-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5
Show all the steps

Answer 1

I don't want someone to just give me the answer I need help figuring it out!

Answer 2

Would this help? http://www.themathpage.com/alg/simultaneous-equations-3.htm

Answer 3

I tried to work the problem out using this method but I didn't get an answer that worked. :/

Answer 4

Can you show me everything you did step-by-step?

Answer 5

i added _2x+2y+3z=0 to 2x+3y+3z=5 to get 5y+6z=5
then i added -2x-y+z=-3 to 2x+3y+3z=5 to get 2y+4z=2 and i am stuck from there

Answer 6

Try equation 3 minus equation 1 then add equation 2

Answer 7

Add 2) and 3)
\[-y + z + 3 y + 3 z = -3 + 5 \]\[2 y+4 z= 2 \]1) add 1) and 3)\[-2 x+2 y+3 z+2 x+3 y+3 z=0+5 \]\[5 y+6 z=5 \]You now have two equations in two unknowns:\[\{2 y+4 z=2,5 y+6 z=5\}\]@Danny_D
Can you take it from here?

Answer 8

that gives me x=5 right @wolfe8

Answer 9

Yeah it should give you x, then substitute x into another equation and do similar things.

Answer 10

My bad, I get x=-1

Answer 11

i am so confused! how do we plug in x=-1 now?

Answer 12

Plug in x=-1 into all equations so now you only have simultaneous equation with 2 unknowns only.

Answer 13

so -2(-1)+2y+3z=0

Answer 14

That's for the first equation. Do the same for the rest. Then you will have 2 unknowns left which should be simple.

Answer 15

my brain is so dead right now, could you help me solve the simple equations too?

Answer 16

Well after that you will be left with equations
2y+3z=-2
-y+z=1
3y+3z+3

Add equation 1 to 2 times equation 2 should give you z.

Answer 17

y+4z=3 times -y+z=1 right?

Answer 18

I meant 2 times equation 2, meaning equation 2 will become -2y+2z=2
Add that to equation 1 and get z.

Answer 19

3z=0

Answer 20

If we did everything right, z is 0 then.

Answer 21

ok then we can go through and put -2x+3=-2 -x+3=1 and 3x+3=3

Answer 22

which makes x=0 as well

Answer 23

We already have x from the first step, remember? Now use z=0 in equation 3 that we get after putting in x.

Answer 24

That should give you y.

Answer 25

thats what i ment x=0 but then i got three different answers for y when i plugged in these numbers!

Answer 26

Then you might want to check our workings. Sorry I can't myself. I'm studying for a test. But what we did is basically the procedure.

Answer 27

thanks for your time

Answer 28

Or you could try robtobey's method up there.