Solve the pair of linear equations by using cross multiplication method
(ii) $(a + 2 b) x + (2 a - b) y = 2, (a - 2 b) x + (2 a + b) y = 3$

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Solution

$(a + 2 b) x + (2 a - b) y = 2$
$(a - 2 b) x + (2 a + b) y = 3$
$\frac{x}{6 a - 3 b - 4 a - 2 b} = \frac{y}{2 a - 4 b - 3 a - 6 b} = \frac{1}{(a + 2 b) (2 a + b) - (2 a - b) (a - 2 b)}$
$\Rightarrow \frac{x}{2 a - 5 b} = \frac{y}{- a - 10 b} = \frac{1}{2 a^{2} + 4 a b + a b + 2 b^{2} - 2 a^{2} + 4 a b + a b - 2 b^{2}}$
$\Rightarrow \frac{x}{2 a - 5 b} = \frac{y}{- a - 10 b} = \frac{1}{10 a b}$
$\Rightarrow \frac{x}{2 a - 5 b} = \frac{1}{10 a b}, \frac{y}{- a - 10 b} = \frac{1}{10 a b}$
$∴ x = \frac{2 a - 5 b}{10 a b}, y = \frac{- a - 10 b}{10 a b}$

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Similar questions

(a + 2 b) x + (2 a - b) y = 2

(a - 2 b) x + (2 a + b) y = 3

(a + 2 b) x + (2 a - b) y = 2

(a - 2 b) x + (2 a + b) y = 3

(a - b) x + (a + b) y = 2 a^{2} - 2 a b^{2}, (a + b) (x + y) = 4 a b

x, y :

(a + 2 b) x + (2 a - b) y = 2, (a - 2 b) x + (2 a + b) y = 3

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