SOLUTION: 5r-2s=13 2r-5s=11 what is the solution of the system?

Algebra ->  Equations -> SOLUTION: 5r-2s=13 2r-5s=11 what is the solution of the system?       Log On


   

Question 147180: 5r-2s=13
2r-5s=11
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%285r-2s=13%2C2r-5s=11%29


Let's solve the system by elimination.



Now in order to solve this system by using elimination/addition, we need to solve (or isolate) one variable. I'm going to solve for s.





In order to solve for one variable, we must eliminate the other variable. So if we wanted to solve for s, we would have to eliminate r (or vice versa).


So lets eliminate r. In order to do that, we need to have both r coefficients that are equal in magnitude but have opposite signs (for instance 2 and -2 are equal in magnitude but have opposite signs). This way they will add to zero. By adding to zero, they can be eliminated.



So to make the r coefficients equal in magnitude but opposite in sign, we need to multiply both r coefficients by some number to get them to an common number. So if we wanted to get 5 and 2 to some equal number, we could try to get them to the LCM.



Since the LCM of 5 and 2 is 10, we need to multiply both sides of the top equation by 2 and multiply both sides of the bottom equation by -5 like this:




2%285r-2s%29=2%2813%29 Multiply the top equation (both sides) by 2
-5%282r-5s%29=-5%2811%29 Multiply the bottom equation (both sides) by -5




Distribute and multiply

10r-4s=26
-10r%2B25s=-55


Now add the equations together. In order to add 2 equations, group like terms and combine them

%2810r-10r%29%2B%28-4s%2B25s%29=26-55

Combine like terms and simplify



cross%2810r-10r%29%2B21s=-29 Notice how the r terms cancel out




21s=-29 Simplify




s=-29%2F21 Divide both sides by 21 to isolate s



Now plug this answer into the top equation 5r-2s=13 to solve for x

5r-2s=13 Start with the first equation



5r-2%28-29%2F21%29=13 Plug in s=-29%2F21




5r%2B58%2F21=13 Multiply



%2821%29%285r%2B58%2F21%29=%2821%29%2813%29 Multiply both sides by the LCM of 21. This will eliminate the fractions (note: if you need help with finding the LCM, check out this solver)



105r%2B58=273 Distribute and multiply the LCM to each side



105r=273-58Subtract 58 from both sides


105r=215 Combine like terms on the right side


r=%28215%29%2F%28105%29 Divide both sides by 105 to isolate r



r=43%2F21 Reduce




So our answer is
r=43%2F21 and s=-29%2F21



which forms the ordered pair