If $2 x + 3 y = 24$ and $2 x - 3 y = 12$ , then the value of $x y$ is ___________.

10

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12

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18

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14

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Solution

The correct option is C $18$
The given equations are,
$2 x + 3 y = 24$ ....(1)
$2 x - 3 y = 12$ ....(2)

Adding Equations (1) and (2), we get
$2 x + 3 y + 2 x - 3 y = 24 + 12$
$\Rightarrow 4 x = 36$
$\Rightarrow x = 9$
Putting $x = 9$ in Equation (1), we get
$2 \times 9 + 3 y = 24$
$\Rightarrow 18 + 3 y = 24$
$\Rightarrow 3 y = 6$
$\Rightarrow y = 2$
Thus $x y = 9 \times 2 = 18$

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