Question

How to solve for x, y, and z by eliminating:
x=1-y
2x=z
2z=-2-y

Answer 1

Okay. make x the subject for the second equation for me please.

Answer 2

Wait you want to do this by elimination?

Answer 3

yes, eliminate the equations until I have solved for one x, y, and

Answer 4

Yeah okay.

Answer 5

Move the -y in the first equation to the other side.

Answer 6

Do the same thing in the third equaiton. Move the -y to the other side.

Answer 7

Always keep the variables on one side of the equation.

Answer 8

variables are the pronumerals or letters: x, y and z.

Answer 9

Give me your rewritten equations for me please after you've done that step.

Answer 10

x+y=1
2x=z
2z+y=-2

Answer 11

What about the second equation? Keep ALL variables to one side.

Answer 12

2x-z=0?

Answer 13

Yep Good work.

Answer 14

Okay so now we have these three equations:
\[x+y=1\]
\[2x-z=0\]
\[2z+y=-2\]
So would we have to multiply the first equation so that the coefficient of x in the first equation is equal to the coefficient of x in the second equation?

Answer 15

-2y-1z=-2

Answer 16

I asked you a question. And that's incorrect.

Answer 17

Okay. Forget about the third equation for now. Eliminate a variable in the first two equations.

Answer 18

yes, you eliminate x by multiplying with -2

Answer 19

YOu can just multiply by 2. That would make your life much easier. And then you can jsut subtract the two equations instead of adding them together....

Answer 20

just*

Answer 21

But if you want to do it that way, that's fine.

Answer 22

Show me what you get when eliminate x.

Answer 23

I'm still getting -2y-1z=-2

-2(x+y)=(1)-2
2x-z=0

Answer 24

Multiply first equation by 2.
\[2x+2y=2\]
Subtract that with the second equation.
\[(2x+2y)-(2x-z)=(2)-(0)\]

Answer 25

What do you get now?

Answer 26

2y-z=2

Answer 27

GOod now eliminate one of the variables using the third equation and the equation you just got.

Answer 28

Do exactly what I did. Just watch for your signs.

Answer 29

y-z=0

Answer 30

? You still have two variables.....I told you to eliminate one....

Answer 31

sorry, messed up my variables

Answer 32

2z+y=-2
2(-z+2y)=(2)2
y=\[\frac{ 2 }{ 5 }\]

Answer 33

correct you aced it. Well done.

Answer 34

you ca just sub that value into the equation to find z.

Answer 35

so I got, \[(-\frac{ 3 }{ 5 },\frac{ 2 }{ 5 },-\frac{ 6 }{ 5 })\]

Answer 36

It's 6/5

Answer 37

Wait nvm you got it right.

Answer 38

Well DOne. All correct.

Answer 39

woo hoo

Answer 40

thanks for helping

Answer 41

No worries.