SOLUTION: the diffrence between two numbers is 11 when the larger number is added to two times the smaller the sum is 59 what are the two numbers

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Question 202045: the diffrence between two numbers is 11 when the larger number is added to two times the smaller the sum is 59 what are the two numbers
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
"the difference between two numbers is 11" means that x-y=11


"the larger number is added to two times the smaller the sum is 59" tells us that 2x%2By=59




Start with the given system of equations:
system%28x-y=11%2Cx%2B2y=59%29


2%28x-y%29=2%2811%29 Multiply the both sides of the first equation by 2.


2x-2y=22 Distribute and multiply.


So we have the new system of equations:
system%282x-2y=22%2Cx%2B2y=59%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:


%282x-2y%29%2B%28x%2B2y%29=%2822%29%2B%2859%29


%282x%2B1x%29%2B%28-2y%2B2y%29=22%2B59 Group like terms.


3x%2B0y=81 Combine like terms.


3x=81 Simplify.


x=%2881%29%2F%283%29 Divide both sides by 3 to isolate x.


x=27 Reduce.


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2x-2y=22 Now go back to the first equation.


2%2827%29-2y=22 Plug in x=27.


-2y=22-54 Subtract 54 from both sides.


-2y=-32 Combine like terms on the right side.


y=%28-32%29%2F%28-2%29 Divide both sides by -2 to isolate y.


y=16 Reduce.


So the solutions are x=27 and y=16.


Which form the ordered pair .


This means that the system is consistent and independent.


So the two numbers are 27 and 16.