SOLUTION: I need help with eliminations please. I have to find out what x or y is to get the other variable. The problem is 18x-18y=0 12x-12y=-12 I've tried

Algebra ->  Algebra  -> Expressions-with-variables -> SOLUTION: I need help with eliminations please. I have to find out what x or y is to get the other variable. The problem is 18x-18y=0 12x-12y=-12 I've tried       Log On

Ad: Algebra Solved!™: algebra software solves algebra homework problems with step-by-step help!
Ad: Algebrator™ solves your algebra problems and provides step-by-step explanations!

   

Question 177434: I need help with eliminations please. I have to find out what x or y is to get the other variable. The problem is 18x-18y=0
12x-12y=-12
I've tried multiplying the top by 12 and the bottom by 12 and i've also tried multiplying the top by 18 and then trying to solve it but both times I still have 2 variables left. How do I use eliminations when if I multiply it I will get the same on both sides and sometimes on top and bottom?
Thank you for helping me.
Found 2 solutions by jim_thompson5910, Mathtut:
Answer by jim_thompson5910(28504) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%2818x-18y=0%2C12x-12y=-12%29


2%2818x-18y%29=2%280%29 Multiply the both sides of the first equation by 2.


36x-36y=0 Distribute and multiply.


-3%2812x-12y%29=-3%28-12%29 Multiply the both sides of the second equation by -3.


-36x%2B36y=36 Distribute and multiply.


So we have the new system of equations:
system%2836x-36y=0%2C-36x%2B36y=36%29


Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:


%2836x-36y%29%2B%28-36x%2B36y%29=%280%29%2B%2836%29


%2836x%2B-36x%29%2B%28-36y%2B36y%29=0%2B36 Group like terms.


0x%2B0y=36 Combine like terms.


0=36Simplify.


Since 0=36 is NEVER true, this means that there are no solutions.


So the system is inconsistent.

Answer by Mathtut(3670) About Me  (Show Source):
You can put this solution on YOUR website!
actually you dont need to multiply by that high of a number...the LCM of 12 and 18 is 36
:
so if you multiply the top by -2 and the bottom by 3 you will eliminate the x terms
:
18x-18y=0
12x-12y=-12
:
-2(18x-18y=0)---->-36x+36y=0
3(12x+12y=-12)--> 36x+36y=-36
:
and now you just add the two equations together thus eliminating the x terms and then solve for y. once you have the solution for y you plug that back into either equation to find x.
:
remember you dont have to multiply both equations by the same number.
:
when you multiply all terms in and equation, by a constant, it doesnt change the equation. in other words x+y=3 is the same linear equation as
3(x+y=3)--->3x+3y=9.