Solve, using cross-multiplication :

4x + 3y = 17

3x - 4y + 6 = 0

Given, equations :

⇒ 4x + 3y = 17 and 3x - 4y + 6 = 0

⇒ 4x + 3y - 17 = 0 …….(1)

⇒ 3x - 4y + 6 = 0 ……..(2)

By cross-multiplication method :

$\Rightarrow \dfrac{x}{3 \times 6 - (-4) \times (-17)} = \dfrac{y}{(-17) \times 3 - 6 \times 4} = \dfrac{1}{4 \times (-4) - 3 \times 3} \\[1em] \Rightarrow \dfrac{x}{18 - 68} = \dfrac{y}{-51 - 24} = \dfrac{1}{-16 - 9} \\[1em] \Rightarrow \dfrac{x}{-50} = \dfrac{y}{-75} = \dfrac{1}{-25} \\[1em] \Rightarrow \dfrac{x}{-50} = \dfrac{1}{-25} \text{ and } \dfrac{y}{-75} = \dfrac{1}{-25} \\[1em] \Rightarrow x = \dfrac{-50}{-25} \text{ and } y = \dfrac{-75}{-25} \\[1em] \Rightarrow x = 2 \text{ and } y = 3.$

Hence, x = 2 and y = 3.