SOLUTION: Heres another one and these are making me feel dumb!! Solve using the elimination method 3r-4s=5 4r+3s=15 Type an ordered pair. Either integer or fractions.

Algebra ->  Inequalities -> SOLUTION: Heres another one and these are making me feel dumb!! Solve using the elimination method 3r-4s=5 4r+3s=15 Type an ordered pair. Either integer or fractions.       Log On


   

Question 299194: Heres another one and these are making me feel dumb!!
Solve using the elimination method
3r-4s=5
4r+3s=15
Type an ordered pair. Either integer or fractions.
Thanks again!!
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-4s=5%2C4r%2B3s=15%29


3%283r-4s%29=3%285%29 Multiply the both sides of the first equation by 3.


9r-12s=15 Distribute and multiply.


4%284r%2B3s%29=4%2815%29 Multiply the both sides of the second equation by 4.


16r%2B12s=60 Distribute and multiply.


So we have the new system of equations:
system%289r-12s=15%2C16r%2B12s=60%29


Why did we just do all that? You'll see below:


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-12s%29%2B%2816r%2B12s%29=%2815%29%2B%2860%29


%289r%2B16r%29%2B%28-12s%2B12s%29=15%2B60 Group like terms.


25r%2B0s=75 Combine like terms.


Notice how the 's' terms add to 0 and cancel out. So we're now left with a simple equation with one unknown.


25r=75 Simplify.


r=%2875%29%2F%2825%29 Divide both sides by 25 to isolate r.


r=3 Reduce.


------------------------------------------------------------------


9r-12s=15 Now go back to the first equation.


9%283%29-12s=15 Plug in r=3.


27-12s=15 Multiply.


-12s=15-27 Subtract 27 from both sides.


-12s=-12 Combine like terms on the right side.


s=%28-12%29%2F%28-12%29 Divide both sides by -12 to isolate s.


s=1 Reduce.


So the solutions are r=3 and s=1.


Which form the ordered pair .


This means that the system is consistent and independent.