Can someone show me how to solve the system by elimination with?

Question

-2x+2y+3z=0
-2x-y+z=-3
2x+3y+3z=5

Answer 1

add the 3rd equation to the 1st and then the 2nd to eliminate x

1 & 3 ... 5y + 6z = 5 ... (A)

2 & 3 ... 2y + 4z = 2 ... (B)
... multiply by 3/2 ... 3y + 6z = 3 ... (C)

subtract (C) from (A) to eliminate z
... 2y = 2

substitute the y-value back to find x and z

Answer 2

So it would go like
-2x+2y+3z=0
2x+3y+3z=5
Equal
0x+5y+6z=5?

-2x-y+z=-3
2x+3y+3z=5
Equal
0x+3y+3z=5

But if I multiply 3/2 with what you got (aka) 2 & 3 ... 2y + 4z = 2 ... (B)

3/2*2=3
3/2*4=6
3/2*2=3

So I’d plug in the variables and get
3y+6z=3

And then subtract
5y + 6z = 5
From
3y + 6z = 3
And get
2y+0z=2

So basically if our variable has 0 it drops (aka) it’s dead? As in we don’t use it?

So I’d get 2y=2... but you said substitute y back to get x and z but how do I do that????

(So basically I have 2 problems with how I just solved this problem #1 I have no clue how you got “B” because I guess I solved it wrong??? And I have no clue on how to substitute y back to find x and z).... I know all I did is somewhat retyped what you said do, but I was showing you why i needed help instead of just being given the answers I needed someone to help explain and guide me step by step so I’d be able to look back and try doing it on my own.

Answer 3

you have found y=1

You also have
5y+6z=5
so, 5+6z = 5, so z=0

Now you have any of the original equations, such as

2x+3y+3z=5
2x+3+0=5
x=1

Answer 4

So does that mean for “B” I was right? Or did you just go with mine?...and I’m still confused on how you found x, for everything else I understand now. Thank you

Answer 5

So it would go like
-2x+2y+3z=0
2x+3y+3z=5
Equal
0x+5y+6z=5?

-2x-y+z=-3
2x+3y+3z=5
Equal
0x+3y+3z=5

But if I multiply 3/2 with what you got (aka) 2 & 3 ... 2y + 4z = 2 ... (B)

3/2*2=3
3/2*4=6
3/2*2=3

So I’d plug in the variables and get
3y+6z=3

And then subtract
5y + 6z = 5
From
3y + 6z = 3
And get
2y+0z=2

So basically if our variable has 0 it drops (aka) it’s dead? As in we don’t use it?

So I’d get 2y=2... but you said substitute y back to get x and z but how do I do that????

(So basically I have 2 problems with how I just solved this problem #1 I have no clue how you got “B” because I guess I solved it wrong??? And I have no clue on how to substitute y back to find x and z).... I know all I did is somewhat retyped what you said do, but I was showing you why i needed help instead of just being given the answers I needed someone to help explain and guide me step by step so I’d be able to look back and try doing it on my own.