SOLUTION: 5x+2y=8 7x+8y=3

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Question 597795: 5x+2y=8
7x+8y=3
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%285x%2B2y=8%2C7x%2B8y=3%29


-4%285x%2B2y%29=-4%288%29 Multiply the both sides of the first equation by -4.


-20x-8y=-32 Distribute and multiply.


So we have the new system of equations:
system%28-20x-8y=-32%2C7x%2B8y=3%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:


%28-20x-8y%29%2B%287x%2B8y%29=%28-32%29%2B%283%29


%28-20x%2B7x%29%2B%28-8y%2B8y%29=-32%2B3 Group like terms.


-13x%2B0y=-29 Combine like terms.


-13x=-29 Simplify.


x=%28-29%29%2F%28-13%29 Divide both sides by -13 to isolate x.


x=29%2F13 Reduce.


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-20x-8y=-32 Now go back to the first equation.


-20%2829%2F13%29-8y=-32 Plug in x=29%2F13.


-580%2F13-8y=-32 Multiply.


13%28-580%2Fcross%2813%29-8y%29=13%28-32%29 Multiply both sides by the LCD 13 to clear any fractions.


-580-104y=-416 Distribute and multiply.


-104y=-416%2B580 Add 580 to both sides.


-104y=164 Combine like terms on the right side.


y=%28164%29%2F%28-104%29 Divide both sides by -104 to isolate y.


y=-41%2F26 Reduce.


So the solutions are x=29%2F13 and y=-41%2F26.


Which form the ordered pair .


This means that the system is consistent and independent.