Solve the following systems of simultaneous linear equations by cross-multiplication method :

3x + 2y = 4

8x + 5y = 9

Given equations can be written as,

3x + 2y - 4 = 0

8x + 5y - 9 = 0

By cross multiplication method,

$\therefore \dfrac{x}{2 \times (-9) - 5 \times (-4)} = \dfrac{y}{(-4) \times 8 - (-9) \times 3} = \dfrac{1}{3 \times 5 - 8 \times 2} \\[1em] \Rightarrow \dfrac{x}{-18 + 20} = \dfrac{y}{-32 + 27} = \dfrac{1}{15 - 16} \\[1em] \Rightarrow \dfrac{x}{2} = \dfrac{y}{-5} = \dfrac{1}{-1} \\[1em] \therefore \dfrac{x}{2} = \dfrac{1}{-1} \text{ and } \dfrac{y}{-5} = \dfrac{1}{-1} \\[1em] \Rightarrow x = -2 \text{ and } y = 5.$

Hence, x = -2 and y = 5.