Question

44 _ x + y + 30 _ x -y = 10 55_x +y + 40_x-y = 13

Answer 1

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$let \: \frac{1}{x + y} = u \: and \frac{1}{x - y} = v \\ 44u + 30v = 10 \\ 55u + 40v = 13 \\ by \: solving \: these \: \: linear \: \: equations \: we \: get \: \\ u = \frac{1}{11} \\ v = \frac{1}{5} \\ \frac{1}{x + y} = \frac{1}{11} \\ x + y = 11 \\ \frac{1}{x - y} = \frac{1}{5} \\ x - y = 5 \\ by \: solving \: x + y = 11 \: and \: x - y = 5 \\ x =8 \\ y = 3$