$2 x - 3 y = - 14$
$3 x - 2 y = - 6$
If $(x, y)$ is a solution to the system of equations above, what is the value of $x y$ ?

- 20

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- 8

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12

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8

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Solution

The correct option is B $12$
Given: $2 x - 3 y = - 14 . . . (1)$
$3 x - 2 y = - 6 . . . (2)$
After adding $(1)$ and $(2)$ equations. we get
$2 x - 3 y + 3 x - 2 y = - 14 - 6$
$\Rightarrow 5 x - 5 y = - 20 \Rightarrow x - y = - 4 . . . (3)$
On subtracting $(1)$ from $(2)$ . we get
$3 x - 2 y - 2 x + 3 y = - 6 + 14$
$\Rightarrow x + y = 8 . . . (4)$
Now adding $(3)$ and $(4)$ . we get
$2 x = 4 \Rightarrow x = 2$
By putting $x = 2$ in $(3)$ , we get
$2 - y = - 4 \Rightarrow y = 6$
$∴ (2, 6)$ is solution of given equations.
Value of $x y = 2 \times 6 = 12$ .

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