SOLUTION: Solve by the elimination method. 7r-5s=-12 5r-7s=76 What is the solution of the system?

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: Solve by the elimination method. 7r-5s=-12 5r-7s=76 What is the solution of the system?      Log On


   

Question 221989: Solve by the elimination method. 7r-5s=-12 5r-7s=76
What is the solution of the system?
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%287r-5s=-12%2C5r-7s=76%29


7%287r-5s%29=7%28-12%29 Multiply the both sides of the first equation by 7.


49r-35s=-84 Distribute and multiply.


-5%285r-7s%29=-5%2876%29 Multiply the both sides of the second equation by -5.


-25r%2B35s=-380 Distribute and multiply.


So we have the new system of equations:
system%2849r-35s=-84%2C-25r%2B35s=-380%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:


%2849r-35s%29%2B%28-25r%2B35s%29=%28-84%29%2B%28-380%29


%2849r%2B-25r%29%2B%28-35s%2B35s%29=-84%2B-380 Group like terms.


24r%2B0s=-464 Combine like terms. Notice how the y terms cancel out.


24r=-464 Simplify.


r=%28-464%29%2F%2824%29 Divide both sides by 24 to isolate r.


r=-58%2F3 Reduce.


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


49r-35s=-84 Now go back to the first equation.


49%28-58%2F3%29-35s=-84 Plug in r=-58%2F3.


-2842%2F3-35s=-84 Multiply.


3%28-2842%2Fcross%283%29-35s%29=3%28-84%29 Multiply both sides by the LCD 3 to clear any fractions.


-2842-105s=-252 Distribute and multiply.


-105s=-252%2B2842 Add 2842 to both sides.


-105s=2590 Combine like terms on the right side.


s=%282590%29%2F%28-105%29 Divide both sides by -105 to isolate s.


s=-74%2F3 Reduce.


So the solutions are r=-58%2F3 and s=-74%2F3