SOLUTION: 3x-2y=13 5x+7y=22

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Question 303286: 3x-2y=13
5x+7y=22
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-2y=13%2C5x%2B7y=22%29


7%283x-2y%29=7%2813%29 Multiply the both sides of the first equation by 7.


21x-14y=91 Distribute and multiply.


2%285x%2B7y%29=2%2822%29 Multiply the both sides of the second equation by 2.


10x%2B14y=44 Distribute and multiply.


So we have the new system of equations:
system%2821x-14y=91%2C10x%2B14y=44%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:


%2821x-14y%29%2B%2810x%2B14y%29=%2891%29%2B%2844%29


%2821x%2B10x%29%2B%28-14y%2B14y%29=91%2B44 Group like terms.


31x%2B0y=135 Combine like terms.


31x=135 Simplify.


x=%28135%29%2F%2831%29 Divide both sides by 31 to isolate x.


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21x-14y=91 Now go back to the first equation.


21%28135%2F31%29-14y=91 Plug in x=135%2F31.


2835%2F31-14y=91 Multiply.


31%282835%2Fcross%2831%29-14y%29=31%2891%29 Multiply both sides by the LCD 31 to clear any fractions.


2835-434y=2821 Distribute and multiply.


-434y=2821-2835 Subtract 2835 from both sides.


-434y=-14 Combine like terms on the right side.


y=%28-14%29%2F%28-434%29 Divide both sides by -434 to isolate y.


y=1%2F31 Reduce.


So the solutions are x=135%2F31 and y=1%2F31.


Which form the ordered pair .


This means that the system is consistent and independent.