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Solve the following pair of equations :- 10/x+y + 2/x-y =4 15/x+y - 5/x-y = -2

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$ Given : $ \frac{10}{x+y} + \frac{2}{x-y} =4 ..(i) \\\\ \frac{15}{x+y} - \frac{5}{x-y} = -2 ...(ii) \\\\ $ assume x+y=p, x-y=q $ \\ 10p + 2q =4 ...(iii)\\ 15 p -5q = -2 ...(iv) \\ 3 \times Equation (iii) - 2 \times Equation (iv) \\ 30p + 6q - 30p + 10 q = 12+ 4\\ 16 q =16 \Rightarrow q=1 \\ p = \frac{1}{5}\\\\ x + y = \frac{1}{5} ...(v)\\\\ x - y = 1 ...(vi)\\\\ $ Equation (v) + Equation (vi) $ \\ 2x= \frac{6}{5} \Rightarrow x= \frac{3}{5}\\\\ y = \frac{-2}{5}

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Ravindra Pindel

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