Question 762862
how can i solve the equations 72x+50y=9xy & 90x+70y=12xy
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72x+50y=9xy
90x+70y=12xy
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Solve both for y
72x+50y=9xy
72x = 9xy - 50y = y*(9x - 50)
y = 72x/(9x-50)
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90x+70y=12xy
45x + 35y = 6xy
45x = 6xy - 35y = y*(6x - 35)
y = 45x/(6x - 35)
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since they both equal y,
72x/(9x-50) = 45x/(6x - 35)
An obvious solution is x = 0 --> y = 0
(0,0) is one.
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72x/(9x-50) = 45x/(6x - 35)
Divide by x
72/(9x-50) = 45/(6x - 35)
8/(9x-50) = 5/(6x - 35)
8(6x-35) = 5(9x-50)
48x - 280 = 45x - 250
3x = 30
x = 10
y = 18
--> (10,18)