Question

I've been stuck on this problem for days. Solve the system by elimination. { -2x + 2y + 3z = 0; -2x - y + z = -3; 2x + 3y + 3z = 5. Any help would be nice! Normally I wouldn't be this stuck :/

Answer 1

Really need help on this :/

Answer 2

I'll help you out.

Answer 3

Thank you!

Answer 4

key is to eliminate a variable to get it into a system of 2 equations with 2 variables, then solve that smaller system with elimination. then by substitution you can find the 3rd variable
@Owlcoffee will demonstrate :)

Answer 5

So we have:
-2x + 2y + 3z = 0
-2x - y + z = -3
2x + 3y + 3z = 5
Let's first pick two equations here, i'll pick the first and the second:
-2x + 2y + 3z = 0
-2x - y + z = -3
I'll multiply the first one by -1 just to eliminate the x's. ending up with:
2x - 2y - 3z = 0
-2x - y + z = -3
I will sum this equations, so the 2x and the -2x will simplify, i'll end with an equation looking like this:
-3y-2z=-3
We have just created an equation with only two variables, but we need to make another one :(

I encourage you to fabricate the other ecuation, it's the same idea. :)

Answer 6

Okay.. I did:
-2x - y + z = -3
2x + 3y + 3z = 5
from that I got 2y + 4z = 2.
So would I write the two new equations like
-3y - 2z = 3
2y + 4z = 2

Answer 7

Good! now solve that 2x2 system :)

Answer 8

Okay! I got
-6 y - 4z = 6
2y + 4z = 5
then -4y = 8 and divided by -4 which got y = -2. So now do I have to find x and z?

Answer 9

You have a equation !
So if you get y the number you have can find both of them !:)

Answer 10

yes, on the 2nd system, replace the value of y to find z.
and on the first 3x3, replace both z and y to get the value of x.

Answer 11

So on the -6y - 4z =6 I would replace the y? or the -2x - y + z= -3? A little confused on this part :s