SOLUTION: What is the system of equations 2r+2s=50 and 2r-s=17?

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Question 175702: What is the system of equations 2r+2s=50 and 2r-s=17?
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%282r%2B2s=50%2C2r-s=17%29


2%282r-s%29=2%2817%29 Multiply the both sides of the second equation by 2.


4r-2s=34 Distribute and multiply.


So we have the new system of equations:
system%282r%2B2s=50%2C4r-2s=34%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:


%282r%2B2s%29%2B%284r-2s%29=%2850%29%2B%2834%29


%282r%2B4r%29%2B%282s%2B-2s%29=50%2B34 Group like terms.


6r%2B0s=84 Combine like terms.


6r=84 Simplify.


r=%2884%29%2F%286%29 Divide both sides by 6 to isolate r.


r=14 Reduce.


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2r%2B2s=50 Now go back to the first equation.


2%2814%29%2B2s=50 Plug in r=14.


28%2B2s=50 Multiply.


2s=50-28 Subtract 28 from both sides.


2s=22 Combine like terms on the right side.


s=%2822%29%2F%282%29 Divide both sides by 2 to isolate s.


s=11 Reduce.


So our answer is r=14 and s=11.


This means that the system is consistent and independent.