SOLUTION: 1/x+1/y=3,1/x-1/y=3

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: 1/x+1/y=3,1/x-1/y=3      Log On


   

Question 1015269: 1/x+1/y=3,1/x-1/y=3
Found 2 solutions by Edwin McCravy, Alan3354:
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
system%281%2Fx%2B1%2Fy=3%2C1%2Fx-1%2Fy=3%29
The main thing NOT to do in a system like this is
to clear of fractions. DO NOT clear of fractions.
Leave them as they are and use elimination just as normal.
If you add the two equations just as they are you get:
2%2Fx=6
Consider the 6 as over 1:
2%2Fx=6%2F1
Cross multiply:
6x=2
x=2%2F6
x=1%2F3
Start over with
system%281%2Fx%2B1%2Fy=3%2C1%2Fx-1%2Fy=3%29
Multiply the 2nd equation through by -1
system%281%2Fx%2B1%2Fy=3%2C-1%2Fx%2B1%2Fy=-3%29
Add them term by term:
2%2Fx=0
2%2Fx=0%2F1
Cross multiply
0x=2
x=cross%282%2F0%29
That is meaningless, so there can be no solution.
Edwin


Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
1/x+1/y=3
1/x-1/y=3
--------
Sub r for 1/x, s for 1/y
r + s = 3
r - s = 3
---------- Add
2r = 6
r = 3 --> x = 1/3
-----------
s = 0 --> y = 1/0
y is undefined --> no solution.