SOLUTION: Solve using elimination 3r-5s=-3 5r+3s=29 find soultions

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Question 201023: Solve using elimination
3r-5s=-3
5r+3s=29
find soultions
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%283r-5s=-3%2C5r%2B3s=29%29


3%283r-5s%29=3%28-3%29 Multiply the both sides of the first equation by 3.


9r-15s=-9 Distribute and multiply.


5%285r%2B3s%29=5%2829%29 Multiply the both sides of the second equation by 5.


25r%2B15s=145 Distribute and multiply.


So we have the new system of equations:
system%289r-15s=-9%2C25r%2B15s=145%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:


%289r-15s%29%2B%2825r%2B15s%29=%28-9%29%2B%28145%29


%289r%2B25r%29%2B%28-15s%2B15s%29=-9%2B145 Group like terms.


34r%2B0s=136 Combine like terms.


34r=136 Simplify.


r=%28136%29%2F%2834%29 Divide both sides by 34 to isolate r.


r=4 Reduce.


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9r-15s=-9 Now go back to the first equation.


9%284%29-15s=-9 Plug in r=4.


36-15s=-9 Multiply.


-15s=-9-36 Subtract 36 from both sides.


-15s=-45 Combine like terms on the right side.


s=%28-45%29%2F%28-15%29 Divide both sides by -15 to isolate s.


s=3 Reduce.


So the solutions are r=4 and s=3.


This means that the system is consistent and independent.