for what values of x, y and z is
2-2x=y
-3z+4x=0
9z-6=-4y true?

Question

for what values of x, y and z is 
2-2x=y
-3z+4x=0
9z-6=-4y true?

anonymous · Answer

Tell me what to do.

anonymous · Answer

can you solve this using substitution? 
can you plug 2-2x=y into 9z-6=-4y so it equals 9z-6=-4(2-2x)?

anonymous · Answer

Multiply first equation by 2 and then add equation 1 with equation 2..

 you will get another equation having y and z as two variables in it..

anonymous · Answer

Yes you can do that..

but it will go longer..

anonymous · Answer

Or you wanna solve this by Substitution  Method??

anonymous · Answer

I rather do it the quickest way :) the actual problem did not specify which was it wants us to solve it

anonymous · Answer

Then you must use Elimination Method...

Multiply first equation by 2 and tell me what did you get??

anonymous · Answer

4-4x=2y?

anonymous · Answer

Yep now add this equation with second one and tell me what are you having now??

anonymous · Answer

3z+4=2y?

anonymous · Answer

It should come -3z there

Right ??

anonymous · Answer

oh yea! sorry -3z+4=2y

anonymous · Answer

Rearrange it so that it must look nice to me... Can you do that?

anonymous · Answer

4-3z=2y?
or 2y+3z=4?

anonymous · Answer

Second one is looking very nice to me..

anonymous · Answer

Variables on one side and constants on other side..

anonymous · Answer

Now rearrange the third equation also.. (of your question)..

anonymous · Answer

9z+4y=6?

anonymous · Answer

or :      4y + 9z = 6..

anonymous · Answer

Now you have :

2y + 3z = 4
4y + 9z = 6


Now multiply first equation with 2..

anonymous · Answer

4y+6z=8?

anonymous · Answer

Now subtract it with 2nd equation and find z..

anonymous · Answer

4y + 6z = 8
4y + 9z = 6

Subtract them..

anonymous · Answer

-2/3?

anonymous · Answer

Yep..
Now find y carefully by putting z in any one equation..

anonymous · Answer

Getting ???

anonymous · Answer

y=1?

anonymous · Answer

No check it one more time, you are going really well..

anonymous · Answer

Let us put it in :

2y + 3z = 4

Here put z = -2/3..

anonymous · Answer

y=3?

anonymous · Answer

Yep now you got it right..

Can you find from first equation now??  (of your question)..

anonymous · Answer

*can you find x..

anonymous · Answer

x=-1/2?

anonymous · Answer

Yep great job @kkvoo 

You are a good learner...

anonymous · Answer

Hooray! Thank you :D

anonymous · Answer

You are welcome dear...