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(vii) 10/(x+y) + 2/(x-y) = 4 15/(x+y) – 5/(x-y) = -2

(vii) 10/(x+y) + 2/(x-y) = 4

15/(x+y) – 5/(x-y) = -2

Grade:12th pass

1 Answers

Pawan Prajapati
askIITians Faculty 60787 Points
2 years ago
Solution: Substituting 1/x+y = m and 1/x-y = n in the given equations, we get, 10m + 2n = 4 => 10m + 2n – 4 = 0 ………………..…..(i) 15m – 5n = -2 => 15m – 5n + 2 = 0 ……………………..(ii) Using cross-multiplication method, we get, m/(4-20) = n/(-60-(20)) = 1/(-50 -30) m/-16 = n/-80 = 1/-80 m/-16 = 1/-80 and n/-80 = 1/-80 m = 1/5 and n = 1 m = 1/(x+y) = 1/5 x+y = 5 …………………………………………(iii) n = 1/(x-y) = 1 x-y = 1……………………………………………(iv) Adding equation (iii) and (iv), we get 2x = 6 => x = 3 …….(v) Putting the value of x = 3 in equation (3), we get y = 2 Hence, x = 3 and y = 2

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