Question 675729
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Hi
Assume you meant:  
2r - s = 10   Or  {{{r = (s+10)/2}}}
rs - s^2 = 12
{{{((s+10)/2)s - s^2 = 12}}} |Multiplying thru by 2 so as all denominators = 1
   (s+10)s - 2s^2 = 24
    s^2 + 10s - 2s^2 = 24
      10s - s^2 = 24
     s^2 - 10s + 24 = 0
factoring
   (s-6)(s-4) = 0
    (s-6) = 0  ,  s = 6  and r = 8
  0r (s-4) = 0 ,  s = 4  and r = 7