SOLUTION: Can you please help me find the real solutions if any for this system? 1/x-1/y=1/4 xy=8 i tried solving for x in the second equation which i got x=8/y and plugging in the va

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Can you please help me find the real solutions if any for this system? 1/x-1/y=1/4 xy=8 i tried solving for x in the second equation which i got x=8/y and plugging in the va      Log On


   

Question 29972: Can you please help me find the real solutions if any for this system?
1/x-1/y=1/4
xy=8
i tried solving for x in the second equation which i got x=8/y and plugging in the value for x in the first equation but i get stuck there. i get 1/x/8/y-1/y=1/4
Answer by longjonsilver(2297) About Me  (Show Source):
You can put this solution on YOUR website!
x = 8/y so that +%281%2Fx%29+-+%281%2Fy%29+=+%281%2F4%29+ becomes

+%28y%2F8%29+-+%281%2Fy%29+=+%281%2F4%29+. Now multiply every term by 8y, to give
+y%5E2+-+8+=+2y+
+y%5E2+-+2y+-+8+=+0+
(y-4)(y+2) = 0

so y-4 = 0 or y+2 = 0
--> y=4 or y = -2

When y=4, so x=8/4 --> x=2
When y=-2, so x=8/-2 --> x=-4

CHECK:
1. for (2,4): +%281%2Fx%29+-+%281%2Fy%29+
+%281%2F2%29+-+%281%2F4%29+
--> 1/4... correct

2. for (-4,-2): +%281%2Fx%29+-+%281%2Fy%29+
+%281%2F-4%29+-+%281%2F-2%29+
+%28-1%2F4%29+%2B+%281%2F2%29+
--> 1/4... correct

jon.