1243x = 729y = 33⇒1243x = 33 and 729y = 33⇒135x = 33 and 36y = 33⇒135x = 33 and 36y = 33⇒3-5x = 33 and 36y = 33⇒-5x = 3 and 6y = 3⇒x = -35 and y = 12Now, 5x + 6y = 5 ×-35 + 6 × 12 = -3 + 3 = 0

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\frac{1}{{(243)}^{x}} = {(729)}^{y} = 3^{3} \Rightarrow \frac{1}{{(243)}^{x}} = 3^{3} and {(729)}^{y} = 3^{3} \Rightarrow \frac{1}{{(3^{5})}^{x}} = 3^{3} and {(3^{6})}^{y} = 3^{3} \Rightarrow \frac{1}{3^{5 x}} = 3^{3} and 3^{6 y} = 3^{3} \Rightarrow 3^{- 5 x} = 3^{3} and 3^{6 y} = 3^{3} \Rightarrow - 5 x = 3 and 6 y = 3 \Rightarrow x = - \frac{3}{5} and y = \frac{1}{2} Now, 5 x + 6 y = 5 \times (- \frac{3}{5}) + 6 \times \frac{1}{2} = - 3 + 3 = 0

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