SOLUTION: 3x+2y=7 +2x-y=4

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Question 196627: 3x+2y=7
+2x-y=4
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%283x%2B2y=7%2C2x-y=4%29


2%282x-y%29=2%284%29 Multiply the both sides of the second equation by 2.


4x-2y=8 Distribute and multiply.


So we have the new system of equations:
system%283x%2B2y=7%2C4x-2y=8%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:


%283x%2B2y%29%2B%284x-2y%29=%287%29%2B%288%29


%283x%2B4x%29%2B%282y%2B-2y%29=7%2B8 Group like terms.


7x%2B0y=15 Combine like terms.


7x=15 Simplify.


x=15%2F7 Divide both sides by 7 to isolate x.


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3x%2B2y=7 Now go back to the first equation.


3%2815%2F7%29%2B2y=7 Plug in x=15%2F7.


45%2F7%2B2y=7 Multiply.


cross%287%29%2845%2Fcross%287%29%29%2B7%282y%29=7%287%29 Multiply EVERY term by the LCD 7 to clear any fractions.


45%2B14y=49 Multiply.


14y=49-45 Subtract 45 from both sides.


14y=4 Combine like terms on the right side.


y=%284%29%2F%2814%29 Divide both sides by 14 to isolate y.


y=2%2F7 Reduce.


So the solutions are x=15%2F7 and y=2%2F7 which form the ordered pair