SOLUTION: 5r-6s=21 6r+5s=74 Please help solve Answer: Solve for r and substitute 5r-6s=21 r=21-5s/5 substitute 5(21-5s/5)-6s=21 105-25s/5-6s=21 -5s-6s=21-105 -11s=-84 s=84/11

Algebra ->  Expressions-with-variables -> SOLUTION: 5r-6s=21 6r+5s=74 Please help solve Answer: Solve for r and substitute 5r-6s=21 r=21-5s/5 substitute 5(21-5s/5)-6s=21 105-25s/5-6s=21 -5s-6s=21-105 -11s=-84 s=84/11       Log On


   

Question 198899: 5r-6s=21
6r+5s=74
Please help solve
Answer: Solve for r and substitute
5r-6s=21
r=21-5s/5
substitute
5(21-5s/5)-6s=21
105-25s/5-6s=21
-5s-6s=21-105
-11s=-84
s=84/11

Found 2 solutions by jim_thompson5910, stanbon:
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-6s=21%2C6r%2B5s=74%29


6%285r-6s%29=6%2821%29 Multiply the both sides of the first equation by 6.


30r-36s=126 Distribute and multiply.


-5%286r%2B5s%29=-5%2874%29 Multiply the both sides of the second equation by -5.


-30r-25s=-370 Distribute and multiply.


So we have the new system of equations:
system%2830r-36s=126%2C-30r-25s=-370%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:


%2830r-36s%29%2B%28-30r-25s%29=%28126%29%2B%28-370%29


%2830r%2B-30r%29%2B%28-36s%2B-25s%29=126%2B-370 Group like terms.


0r%2B-61s=-244 Combine like terms.


-61s=-244 Simplify.


s=%28-244%29%2F%28-61%29 Divide both sides by -61 to isolate s.


s=4 Reduce.


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


30r-36s=126 Now go back to the first equation.


30r-36%284%29=126 Plug in s=4.


30r-144=126 Multiply.


30r=126%2B144 Add 144 to both sides.


30r=270 Combine like terms on the right side.


r=%28270%29%2F%2830%29 Divide both sides by 30 to isolate r.


r=9 Reduce.


So the solutions are r=9 and s=4.


This means that the system is consistent and independent.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
5r-6s=21
6r+5s=74
---------------
Multiply thru the 1st by 5 and the 2nd by 6 to get:
25r - 30s = 105
36r + 30s = 444
---------------------
Add to get:
61r = 549
r = 9
--------------
Substitute to solve for "s":
5*9 -6s = 21
45 -6s = 21
-6s = -24
s = 6
===================
Cheers,
Stan H.