SOLUTION: 1/x+1/y=8/15 1/x-1/y=2/15 solve the system I keep getting x=1/3 and y=1/30

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Question 463611: 1/x+1/y=8/15
1/x-1/y=2/15
solve the system
I keep getting x=1/3 and y=1/30
Found 2 solutions by graphmatics, Gogonati:
Answer by graphmatics(170) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/y=8/15
1/x-1/y=2/15
We will first solve the system for x. First we multiply the first equation by y and get
1/x = 8/15 -1/y
1/x = (8/15)(y/y) -(1/y)(15/15)
1/x = (8y/15y) - (15/15y)
1/x = (8y-15)/(15y)
Now substitute the value of 1/x into equation 2 and get
(8y-15)/(15y) - 1/y = 2/15
Multiply this equation by y and get
y(8y-15)/15y - y(1/y) = y(2/15)
(8y-15)/15 - 1 = 2y/15
8y/15 - 15/15 -1 - 2y/15 =0
8y/15 - 2y/15 = 2
6y/15 = 2
y = (15/6)2
y = 15/3 = 5
Substitute y = 5 into the first equation and solve the first equation for x.
1/x = 8/15 - 1/y
1/x = 8/15 - 1/5
1/x = 8/15 - 3/15
1/x = 5/15
1/x = 1/3
x = 3

Answer by Gogonati(855) About Me  (Show Source):
You can put this solution on YOUR website!
Just add them together and get:2%2Fx=10%2F15 => x=3.Plugging x=3 in the
first equation we get:1%2F3%2B1%2Fy=8%2F15 => 1%2Fy=3%2F15=>y=5.
The solution is the ordered pair (3, 5).