xy/x+y =1/5 xy/x-y =1/9 method of elemination
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Value of x = -1/2 and y = 1/7 for xy/(x + y) = 1/5 , xy/(x - y) = 1/9
Given:
- xy/(x + y) = 1/5
- xy/(x - y) = 1/9
To Find:
- Solve for x and y using elimination method
Solution:
Step 1:
Rewrite equations taking reciprocals both sides
(x + y)/xy = 5 => 1/y + 1/x = 5 Eq1
(x - y)/xy = 9 => 1/y - 1/x = 9 Eq2
Step 2:
Add both equations and eliminates and solve for
2/y = 5 + 9
=> 2/y = 14
=> 1/y = 7
=> y = 1/7
Step 3:
Eq1 - Eq2 to eliminate y and solve for x
2/x = 5 - 9
=> 2/x = -4
=> 1/x = -2
=> x = -1/2
Value of x = -1/2 and y = 1/7
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