SOLUTION: Solve by the elimination method. 7r-3s=3 3r+7s=51 I think there is no solution but I'm not sure if I'm correct.

Algebra ->  Equations -> SOLUTION: Solve by the elimination method. 7r-3s=3 3r+7s=51 I think there is no solution but I'm not sure if I'm correct.      Log On


   

Question 547239: Solve by the elimination method.
7r-3s=3
3r+7s=51
I think there is no solution but I'm not sure if I'm correct.
Found 2 solutions by mathie123, josmiceli:
Answer by mathie123(224) About Me  (Show Source):
You can put this solution on YOUR website!
There are a few ways to do this, depending on what variable you want to eliminate. Just to make it simple, I will eliminate my r.
7r-3s=3 (1)
3r%2B7s=51 (2)
I will multiply my equation (1) by 3 (the number in front of r in equation (2)), and my equation (2) by 7 (you guessed it.... the number in front of r in equation (1)). This leaves:
21r-9s=9 (3)
21r%2B49s=357 (4)
Now Subtracting equation (4) by equation (3) we get:
%2821r-9s%29-%2821r%2B49s%29=9-357
-9s-49s=-348
-58s=-348
-58s%2F-58=-348%2F-58
s=6
Now we can substitute this value of s into any of the equations (1)-(4). I will put it into equation (1).
7r-3%2A6=3
7r-18=3
7r-18%2B18=3%2B18
7r=21
7r%2F7=21%2F7
r=3

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
(1) +7r+-+3s+=+3+
(2) +3r+%2B+7s+=+51+
Multiply both sides of (1) by 7
Multiply both sides of (2) by 3
Then add the equations
(1) +49r+-+21s+=+21+
(2) +9r+%2B+21s+=+153+
+58r+=+174+
+r+=+3+
and, since
(1) +7r+-+3s+=+3+
(1) +7%2A3+-+3s+=+3+
(1) +3s+=+21+-+3+
(1) +3s+=+18+
(1) +s+=+6+
Check answers:
(2) +3r+%2B+7s+=+51+
(2) +3%2A3+%2B+7%2A6+=+51+
(2) +9+%2B+42+=+51+
(2) +51+=+51+
OK