SOLUTION: Solve by the elimination method 2r-5s=-33 5r+2s=48 I think the answer is that there is no solution but I am not sure. Please someone help me to solve this

Algebra ->  Coordinate Systems and Linear Equations -> SOLUTION: Solve by the elimination method 2r-5s=-33 5r+2s=48 I think the answer is that there is no solution but I am not sure. Please someone help me to solve this      Log On


   

Question 388335: Solve by the elimination method
2r-5s=-33
5r+2s=48
I think the answer is that there is no solution but I am not sure. Please someone help me to solve this
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-5s=-33%2C5r%2B2s=48%29


2%282r-5s%29=2%28-33%29 Multiply the both sides of the first equation by 2.


4r-10s=-66 Distribute and multiply.


5%285r%2B2s%29=5%2848%29 Multiply the both sides of the second equation by 5.


25r%2B10s=240 Distribute and multiply.


So we have the new system of equations:
system%284r-10s=-66%2C25r%2B10s=240%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:


%284r-10s%29%2B%2825r%2B10s%29=%28-66%29%2B%28240%29


%284r%2B25r%29%2B%28-10s%2B10s%29=-66%2B240 Group like terms.


29r%2B0s=174 Combine like terms.


29r=174 Simplify.


r=%28174%29%2F%2829%29 Divide both sides by 29 to isolate r.


r=6 Reduce.


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4r-10s=-66 Now go back to the first equation.


4%286%29-10s=-66 Plug in r=6.


24-10s=-66 Multiply.


-10s=-66-24 Subtract 24 from both sides.


-10s=-90 Combine like terms on the right side.


s=%28-90%29%2F%28-10%29 Divide both sides by -10 to isolate s.


s=9 Reduce.


So the solutions are r=6 and s=9.


This means that the system is consistent and independent.


If you need more help, email me at jim_thompson5910@hotmail.com

Also, feel free to check out my tutoring website

Jim