Solve 2x + y = 35, 3x + 4y = 65. Hence, find the value of $\dfrac{x}{y}.$

Given,

2x + y = 35 ……(i)

3x + 4y = 65 ……(ii)

From (i) we get,

y = 35 - 2x ……(iii)

Substituting value of y from eqn. (iii) in eqn. (ii) we get,

⟹ 3x + 4(35 - 2x) = 65

⟹ 3x + 140 - 8x = 65

⟹ 140 - 5x = 65

⟹ 5x = 140 - 65

⟹ 5x = 75

⟹ x = 15.

Substituting value of x in eqn. (iii) we get,

⟹ y = 35 - 2x = 35 - 2(15) = 35 - 30 = 5.

⟹ $\dfrac{x}{y} = \dfrac{15}{5} = 3.$

Hence, x = 15, y = 5 and $\dfrac{x}{y} = 3.$