SOLUTION: I need help with this one. I cannot seem to understand it. I have tried for about an hour and a half and nothing is coming out of it. I am stuck. Can amyone help me solve this one?

Algebra ->  Linear-equations -> SOLUTION: I need help with this one. I cannot seem to understand it. I have tried for about an hour and a half and nothing is coming out of it. I am stuck. Can amyone help me solve this one?      Log On


   

Question 209825: I need help with this one. I cannot seem to understand it. I have tried for about an hour and a half and nothing is coming out of it. I am stuck. Can amyone help me solve this one?
2x/3 + 3y/4 = 11/12, x/3 + 7y/18 = 1/2
(solve using elimination method)
Your help is greatly appreciated.

Answer by tutor_paul(519) About Me  (Show Source):
You can put this solution on YOUR website!
Equation #1: 2x/3 + 3y/4 = 11/12
Equation #2: x/3 + 7y/18 = 1/2
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Multiply each and every term of Equation #2 by 2. We will call the result Equation #3. Why are we doing this? Because you will then have a 2x/3 term in each equation. Then you can subtract one equation from the other and "eliminate" the x term. Note that multiplying both sides of an equation by the same number does not change the equation, so it is a legal thing to do!
Equation #3: 2x%2F3%2B14y%2F18=1
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Next, subtract the newly developed Equation #3 from Equation #1:
%282x%2F3-2x%2F3%29%2B%283y%2F4-14y%2F18%29=%2811%2F12-1%29
2x%2F3-2x%2F3=0 so you can rewrite the equation and solve for y:
%283y%2F4-14y%2F18%29=%2811%2F12-1%29
Simplify Left side; LCD=36...
27y%2F36-28y%2F36=%2811%2F12-1%29
-y%2F36=%2811%2F12-1%29
Simplify Right Side; LCD=12...
-y%2F36=%2811%2F12-12%2F12%29
-y%2F36=-1%2F12
Solve for y:
-y=-36%2F12
-y=-3
highlight%28y=3%29
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Now that you have solved for y, simply substitute that value back into Equation #1 and solve for x. I will leave that part of the problem to you.
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Good Luck,
tutor_paul@yahoo.com