Solve each of the following systems of equations by using the method of cross multiplication:

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

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Solution

$\frac{x}{3 b (2 a + b) - 2 b (a + 2 b)} = \frac{y}{3 a (a + 2 b) - 2 a (2 a + b)} = \frac{- 1}{4 a b - 9 a b} \Rightarrow \frac{x}{6 a b + 3 b^{2} - 2 a b - 4 b^{2}} = \frac{y}{3 a^{2} + 6 a b - 4 a^{2} - 2 a b} = \frac{- 1}{- 5 a b} \Rightarrow \frac{x}{4 a b - b^{2}} = \frac{y}{4 a b - a^{2}} = \frac{1}{5 a b} \Rightarrow \frac{x}{4 a b - b^{2}} = \frac{1}{5 a b}, \frac{y}{4 a b - a^{2}} = \frac{1}{5 a b} \Rightarrow x = \frac{b (4 a - b)}{5 a b}, y = \frac{a (4 b - a)}{5 a b} \Rightarrow x = \frac{4 a - b}{5 a}, y = \frac{4 b - a}{5 b}$

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