SOLUTION: 5x-2y=37 3x+4y=9 It is all one problem setup like above.We have tried to add them together and tried to figure out x and y separately. This is my student's problem and I thought

Algebra ->  Algebra  -> Coordinate Systems and Linear Equations -> SOLUTION: 5x-2y=37 3x+4y=9 It is all one problem setup like above.We have tried to add them together and tried to figure out x and y separately. This is my student's problem and I thought      Log On

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Question 175132: 5x-2y=37
3x+4y=9
It is all one problem setup like above.We have tried to add them together and tried to figure out x and y separately. This is my student's problem and I thought I would see how it is done step by step and then we can work on the rest of his assigned problems.
Answer by jim_thompson5910(28593) About Me  (Show Source):
You can put this solution on YOUR website!

Start with the given system of equations:
system%285x-2y=37%2C3x%2B4y=9%29


2%285x-2y%29=2%2837%29 Multiply the both sides of the first equation by 2.


10x-4y=74 Distribute and multiply.


So we have the new system of equations:
system%2810x-4y=74%2C3x%2B4y=9%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:


%2810x-4y%29%2B%283x%2B4y%29=%2874%29%2B%289%29


%2810x%2B3x%29%2B%28-4y%2B4y%29=74%2B9 Group like terms.


13x%2B0y=83 Combine like terms. Notice how the y terms cancel out.


13x=83 Simplify.


x=%2883%29%2F%2813%29 Divide both sides by 13 to isolate x.


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10x-4y=74 Now go back to the first equation.


10%2883%2F13%29-4y=74 Plug in x=83%2F13.


830%2F13-4y=74 Multiply.


13%28830%2Fcross%2813%29-4y%29=13%2874%29 Multiply both sides by the LCD 13 to clear any fractions.


830-52y=962 Distribute and multiply.


-52y=962-830 Subtract 830 from both sides.


-52y=132 Combine like terms on the right side.


y=%28132%29%2F%28-52%29 Divide both sides by -52 to isolate y.


y=-33%2F13 Reduce.


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Answer:


So the solutions are x=%2883%29%2F%2813%29 and y=-33%2F13


which forms the ordered pair