If $2^{x} + 3^{y} = 17, 2^{x + 2} - 3^{y + 1} = 5$ then value of $x$ and $y$ is

x = 2, y = 3

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x = 2, y = 9

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x = 3, y = 2

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x = 9, y = 2

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Solution

The correct option is A $x = 3, y = 2$
Given $2^{x} + 3^{y}$ =17 , $2^{x + 2} - 3^{y + 1}$ =5
by observation, we can say that at $x = 3$ $y = 2$
$\Rightarrow 2^{3} + 3^{2} = 17$
and $2^{5} - 3^{3} = 32 - 27 = 5 = 5$
$∴ x = 3 y = 2$

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