If $2 p + 3 q = 18$ and $4 p^{2} + 4 p q - 3 q^{2} - 36 = 0$ then what is $(2 p + q)$ equal to?

6

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7

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10

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20

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Solution

The correct option is A $10$
$2 p + 3 q = 18 ⟹ p = \frac{18 - 3 q}{2} 4 p^{2} + 4 p q - 3 q^{2} - 36 = 0$

$⟹ 4 {(\frac{18 - 3 q}{2})}^{2} + 4 (\frac{18 - 3 q}{2}) q - 3 q^{2} - 36 = 0 ⟹ 324 - 36 = (108 - 36) q ⟹ 72 q = 288 ⟹ q = 4 ⟹ p = \frac{18 - 12}{2} = 3 ⟹ 2 p + q = 2 (3) + 4 = 10$

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