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

2x - 5y = -1

3x + y = 7

Given equations can be written as,

2x - 5y + 1 = 0

3x + y - 7 = 0

By cross multiplication method,

$\therefore \dfrac{x}{-5 \times (-7) - 1 \times 1} = \dfrac{y}{1 \times 3 - (-7) \times 2} = \dfrac{1}{2 \times 1 - 3 \times -5}\\[1em] \Rightarrow \dfrac{x}{35 - 1} = \dfrac{y}{3 - (-14)} = \dfrac{1}{2 - (-15)}\\[1em] \Rightarrow \dfrac{x}{34} = \dfrac{y}{3 + 14} = \dfrac{1}{2 + 15}\\[1em] \Rightarrow \dfrac{x}{34} = \dfrac{y}{17} = \dfrac{1}{17}\\[1em] \Rightarrow \dfrac{x}{34} = \dfrac{1}{17} \text{ and } \dfrac{y}{17} = \dfrac{1}{17}\\[1em] \Rightarrow x = \dfrac{34}{17} \text{ and }y = \dfrac{17}{17}\\[1em] \Rightarrow x = 2 \text{ and }y = 1.$

Hence, x = 2 and y = 1.