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

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) (Show Source): You can put this solution on YOUR website!
Start with the second equation.

Rearrange the terms.

So we now have the system of equations:

Multiply the both sides of the second equation by -5.

Distribute and multiply.

So we have the new system of equations:

Now add the equations together. You can do this by simply adding the two left sides and the two right sides separately like this:

Group like terms.

Combine like terms.

Simplify.

Divide both sides by to isolate .

Reduce.

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

Now go back to the first equation.

Plug in .

Multiply.

Subtract 3 from both sides.

Combine like terms.

Divide both sides by -10.

Reduce

So the solutions are and .

Which form the ordered pair .

This means that the system is consistent and independent.

Answer by RAY100(1637) (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
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