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Question
Solve the following systems of 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`
Let `1/(x + y) = p and 1/(x - y) = q`
The given equations reduce to:
10p + 2q = 4
=> 10p + 2q - 4 = 0 ....(1)
15p - 5q = -2
=> 15p - 5q + 2 = 0 ...(2)
Using cross-multiplication method, we obtain:
`p.(4- 20) = q/(-60-20) = 1/(-50-30)`
`p/(-16) = q/(-80) = 1/(-80)`
p = 1/5 and q =1
p = 1/(x + y) = 1/5 and `q = 1/(x - y) = 1`
x + y = 5 .....(3)
x - y = 1 ....(4)
Adding equation (3) and (4), we obtain:
2x = 6
x = 3
Substituting the value of x in equation (3), we obtain:
y = 2
∴ x = 3, y = 2
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