Solve the following pairs of linear equations by cross multiplication method:
$(a + 2 b) x + (2 a - b) y = 2$ and $(a - 2 b) x + (2 a + b) y = 3$

x = \frac{b - 2 a}{10 a b}, y = \frac{a + 10 b}{10 a b}

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x = \frac{5 b - 2 a}{2 a b}, y = \frac{a + 10 b}{10 a b}

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x = \frac{5 b - 2 a}{10 a b}, y = \frac{a + 3 b}{10 a b}

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None of these

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Solution

The correct option is D None of these
The given equations are
$(a + 2 b) x + 2 a - b y = 2$ and
$(a - 2 b) x + (2 a + b) y = 3$
Applying cross multiplication method,
$\frac{x}{3 \times (2 a - b) - 2 \times (2 a + b)} = \frac{- y}{(a + 2 b) \times 3 - 2 \times (a - 2 b)} = \frac{1}{(a + 2 b) (2 a + b) - (2 a - b) (a - 2 b)} . ⟹ \frac{x}{2 a - 5 b} = \frac{- y}{a + 10 b} = \frac{1}{10 a b} . ∴ x = \frac{2 a - 5 b}{10 a b}, y = - \frac{a + 10 b}{10 a b} .$
Ans- Option $D$ .

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