$I f 3 x - 7 y = 10 a n d x y = - 1, f i n d t h e v a l u e o f 9 x^{2} + 49 y^{2}$

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Solution

$3 x - 7 y = 10, x y = - 1$

$3 x - 7 y = 10$

Squaring both sides,

$(3 x - 7 y)^{2} = (10)^{2}$

$\Rightarrow (3 x)^{2} + (7 y)^{2} - 2 \times 3 x \times 7 y = 100 \Rightarrow 9 x^{2} + 49 y^{2} - 42 x y = 100 \Rightarrow 9 x^{2} + 49 y^{2} - 42 (- 1) = 100 \Rightarrow 9 x^{2} + 49 y^{2} + 42 = 100 ∴ 9 x^{2} + 49 y^{2} = 100 - 42 = 58$

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