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3-2-37 elimination method with fractions
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    When doing this problem, the easiest way I can tell you is to get rid of the fractions first. So if I multiply that entire equation through by a common denominator of 10 and the second equation all the way through by a common denominator of six. So if I have 10 * 2 X over 5 + 10 * y / 2 equal 10 * 3, this is going to give me a new equation that 10 is understood over one. So five goes into 10 twice. 2 * 2 X would give me 4X that 10 is understood over 1-2 goes into ten five times. So we get 5 Y 10 * 3 is 30. So that's our new equation. One, it's an equivalent. The next equation I'm going to multiply through by 6. So 6 * X / 2 - 6 * y / 6 = 6 * 6. That six is understood over one. So two goes into six three times, so we get three X - 6 / 1. Six goes into six once, so we get minus Y 6 * 6 is 36. So these are our new equations. We have four X + 5 Y equal 30 and three X -, y equal 36. We want to get the coefficients the same. So if I look at the YS, those are almost the same if I multiply the bottom one through by a negative or by A5. So if I multiply that whole equation through by 5, I get 15 X -5 Y equaling 180. If I leave the top equation, just like it is four X + 5 Y equal 30 and add the two equations, now we get nineteen X = 210. So X is going to be 210 nineteenths. Now I could take this and put it back in there and simplify, but that seems like that might be kind of an icky number using nineteenths. So I'm going to go back to the beginning and instead of eliminating the YS, I'm going to try to eliminate these X's. So if I take this top equation and multiply it by three I would get 12X plus 15 Y equal 90. And if I take the second equation and multiply it by a -4, we get -12 X plus 4Y equaling negative for 144. So that now when I add these together the X's cancel and we get 19 Y equaling -54 or Y equal -54 nineteenths. So our ordered pair should be 210 nineteenths -54 nineteenths.