Question 143508
Minor error is causing you grief

2(r+c)=30--->2r+2c=30-->6r+6c=90 
3(r-c)=30---->3r-3c=30--> 6r+6c=60   <-- you changed - to + here
3(r-c)=30---->3r-3c=30--> 6r-6c=60   should be this

Now just use elimination to solve. See here for a video on solving systems of equations. http://collabvsl.wetpaint.com/page/Solving+Systems+of+Equations

6r + 6c = 90
6r - 6c = 60
------------
12r     = 150
r = 12.5

r+c = 15 
12.5 + c = 15
c = 2.5

Does that check out?