SOLUTION: 7x-8y=11 8x-7y=7

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Question 551102: 7x-8y=11
8x-7y=7
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%287x-8y=11%2C8x-7y=7%29


7%287x-8y%29=7%2811%29 Multiply the both sides of the first equation by 7.


49x-56y=77 Distribute and multiply.


-8%288x-7y%29=-8%287%29 Multiply the both sides of the second equation by -8.


-64x%2B56y=-56 Distribute and multiply.


So we have the new system of equations:
system%2849x-56y=77%2C-64x%2B56y=-56%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:


%2849x-56y%29%2B%28-64x%2B56y%29=%2877%29%2B%28-56%29


%2849x%2B-64x%29%2B%28-56y%2B56y%29=77%2B-56 Group like terms.


-15x%2B0y=21 Combine like terms.


-15x=21 Simplify.


x=%2821%29%2F%28-15%29 Divide both sides by -15 to isolate x.


x=-7%2F5 Reduce.


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49x-56y=77 Now go back to the first equation.


49%28-7%2F5%29-56y=77 Plug in x=-7%2F5.


-343%2F5-56y=77 Multiply.


5%28-343%2Fcross%285%29-56y%29=5%2877%29 Multiply both sides by the LCD 5 to clear any fractions.


-343-280y=385 Distribute and multiply.


-280y=385%2B343 Add 343 to both sides.


-280y=728 Combine like terms on the right side.


y=%28728%29%2F%28-280%29 Divide both sides by -280 to isolate y.


y=-13%2F5 Reduce.


So the solutions are x=-7%2F5 and y=-13%2F5.


Which form the ordered pair .


This means that the system is consistent and independent.