$5 x + 7 y = 9$ and $7 x + 5 y = 21$ , then what is the value of $x - y$

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Solution

$5 x + 7 y = 9 ⟹ 35 x + 49 y = 63 \dots (1) 7 x + 5 y = 21 ⟹ 35 x + 25 y = 105 \dots (2) (1) - (2) 49 y - 25 y = 63 - 105 24 y = - 42 y = \frac{- 7}{4} 5 x + 7 (- \frac{7}{4}) = 9 20 x - 49 = 36 20 x = 36 + 49 20 x = 85 x = \frac{17}{4} x - y = \frac{17}{4} + \frac{7}{4} = \frac{24}{4} = 6$

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