Question 177434
actually you dont need to multiply by that high of a number...the LCM of 12 and 18 is 36
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so if you multiply the top by -2 and the bottom by 3 you will eliminate the x terms
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18x-18y=0
12x-12y=-12
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-2(18x-18y=0)---->-36x+36y=0
 3(12x+12y=-12)--> 36x+36y=-36
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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.
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remember you dont have to multiply both equations by the same number.
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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.