SOLUTION: how can i solve the equations 72x+50y=9xy & 90x+70y=12xy

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Question 762862: how can i solve the equations 72x+50y=9xy & 90x+70y=12xy

Found 2 solutions by Alan3354, sachi:
Answer by Alan3354(69443) (Show Source):
You can put this solution on YOUR website!
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)

Answer by sachi(548) (Show Source):
You can put this solution on YOUR website!
72x+50y=9xy ..............1
90x+70y=12xy..............2
now dividing both eqns by xy on both sides we will get
72/y+50/x=9..........3
90/y+70/x=12.........4
multiplying eqn 3 by 10 & eqn 4 by 8 we get
720/y+500/x=90.......5
720/y+560/x=96
- - -
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-60/x=-6
or x=10
putting this value in eqn 3
72/y+50/10=9
or 72/y=9-5=4
or y=72/4=18