Solve the following system of equations by using the method of cross multiplication:

8x − 3y = 12, 5x = 2y + 7

Given,

Equations:

⇒ 8x − 3y - 12 = 0

⇒ 5x - 2y - 7 = 0

By cross-multiplication method,

$\Rightarrow \dfrac{x}{(-3) \times (-7) - (-2) \times (-12)} = \dfrac{y}{(-12) \times (5) - (-7) \times (8)} = \dfrac{1}{(8) \times (-2) - (5) \times (-3)} \\[1em] \Rightarrow \dfrac{x}{21 - 24} = \dfrac{y}{-60 + 56} = \dfrac{1}{-16 + 15} \\[1em] \Rightarrow \dfrac{x}{-3} = \dfrac{y}{-4} = \dfrac{1}{-1} \\[1em] \Rightarrow \dfrac{x}{-3} = \dfrac{1}{-1} \text{ and } \dfrac{y}{-4} = \dfrac{1}{-1} \\[1em] \Rightarrow x = \dfrac{-3}{-1} \text{ and } y = \dfrac{-4}{-1} \\[1em] \Rightarrow x = 3 \text{ and } y = 4.$

Hence, x = 3 and y = 4.