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# Solve the following pairs of equations by reducing them to a pair of linear equations: (vii) 10/(x+y) + 2/(x-y) = 4 15/(x+y) – 5/(x-y) = -2 Q.1(7)

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The best question of exercise 3.6 of math of pair of linear equations in two variables, How i solve this question Solve the following pairs of equations by reducing them to a pair of linear equations: (vii) 10/(x+y) + 2/(x-y) = 4 15/(x+y) – 5/(x-y) = -2

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1. 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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