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Question
Solve the following pairs of equations by reducing them to a pair of linear equations
`10/(x+y) + 2/(x-y) = 4`
`15/(x+y) - 5/(x-y) = -2`
Solution
`10/(x+y) + 2/(x-y) = 4`
`15/(x+y) - 5/(x-y) = -2`
Putting `1/x+y = p ` in the given equations, we get:
10p + 2q = 4
⇒ 10p + 2q - 4 = 0 ... (i)
15p - 5q = -2
⇒ 15p - 5q + 2 = 0 ... (ii)
Using cross multiplication, we get
`p/(4-20) = q/(-60-(-20)) = 1/(-50-30)`
`p/-16 = q/-80 = 1/-80`
`p/-16 = 1/-80 `
p = 1/5 and q = 1
`p = 1/(x+y) = 1/5 and q = 1/(x-y) = 1`
x + y = 5 ... (iii)
and x - y = 1 ... (iv)
Adding equation (iii) and (iv), we get
2x = 6
x = 3 .... (v)
Putting value of x in equation (iii), we get
y = 2
Hence, x = 3 and y = 2
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