SOLUTION: can you please help me solve this equation... 10r-9s=18 6s+2r=1 its either a substitution problem or you add or subtract.. i have tried and tried to get this answer but i

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: can you please help me solve this equation... 10r-9s=18 6s+2r=1 its either a substitution problem or you add or subtract.. i have tried and tried to get this answer but i      Log On


   

Question 191761: can you please help me solve this equation...
10r-9s=18
6s+2r=1
its either a substitution problem or you add or subtract..
i have tried and tried to get this answer but i can't seem to get it..
thank you so much for helping!
Found 2 solutions by jim_thompson5910, RAY100:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
6s%2B2r=1 Start with the second equation.


2r%2B6s=1 Rearrange the terms.


So we now have the system of equations:


system%2810r-9s=18%2C2r%2B6s=1%29



-5%282r%2B6s%29=-5%281%29 Multiply the both sides of the second equation by -5.


-10r-30s=-5 Distribute and multiply.


So we have the new system of equations:

system%2810r-9s=18%2C-10r-30s=-5%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:


%2810r-9s%29%2B%28-10r-30s%29=%2818%29%2B%28-5%29


%2810r%2B-10r%29%2B%28-9s%2B-30s%29=18%2B-5 Group like terms.


0r%2B-39s=13 Combine like terms.


-39s=13 Simplify.


s=%2813%29%2F%28-39%29 Divide both sides by -39 to isolate s.


s=-1%2F3 Reduce.


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


10r-9s=18 Now go back to the first equation.


10r-9%28-1%2F3%29=18 Plug in s=-1%2F3.


10r%2B3=18 Multiply.


10r=18-3 Subtract 3 from both sides.


10r=15 Combine like terms.


r=15%2F10 Divide both sides by -10.


r=3%2F2 Reduce


So the solutions are r=3%2F2 and s=-1%2F3.


Which form the ordered pair .


This means that the system is consistent and independent.




Answer by RAY100(1637) About Me  (Show Source):
You can put this solution on YOUR website!
1) 10R-9S = 18
2) 2R +6S =1
mult (2) by 5
2a) 10R +30S =5
subst ( 2a) from (1)
-39S =13
S= -1/3
subst in (2)
2R + 6(-1/3) = 1
2R -2 =1
2R = 3
R=3/2
check
6(-1/3) + 2 ( 3/2) = 1
-2 +3 =1 ok
10 (3/2) -9(-1/3) =18
15 +3 = 18 ok