SOLUTION: a(y-c) =b(y-c) solve for y

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Question 1045123: a(y-c) =b(y-c) solve for y
Found 2 solutions by jim_thompson5910, ikleyn:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
a%28y-c%29+=b%28y-c%29


a%2Ay-a%2Ac+=b%2Ay-b%2Ac Distribute


a%2Ay-a%2Ac-b%2Ay+=b%2Ay-b%2Ac-b%2Ay Subtract b*y from both sides


a%2Ay-a%2Ac-b%2Ay+=-b%2Ac


a%2Ay-a%2Ac-b%2Ay%2Ba%2Ac+=-b%2Ac%2Ba%2Ac Add a*c to both sides


a%2Ay-b%2Ay+=-b%2Ac%2Ba%2Ac


a%2Ay-b%2Ay+=+a%2Ac-b%2Ac


y%2A%28a-b%29+=c%2A%28a-b%29 Factor (ie, follow the distribution rule in reverse)


%28y%2A%28a-b%29%29%2F%28a-b%29+=%28c%2A%28a-b%29%29%2F%28a-b%29 Divide both sides by (a-b) to isolate y





Notice how the (a-b) terms cancel


y+=+c


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So the final answer is y+=+c


Note: a%3C%3Eb to avoid dividing by zero


Answer by ikleyn(52805) About Me  (Show Source):
You can put this solution on YOUR website!
.
a(y-c) =b(y-c) solve for y
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Answer.  If a =/= b, then the only solution is y = c.
         If a = b, then any "y" is the solution (infinitely many solutions).