Solve the following pair of linear equations by the substitution method.

s - t = 3 and $\dfrac{s}{3} + \dfrac{t}{2} = 6$

Given,

s - t = 3 ………(1)

$\dfrac{s}{3} + \dfrac{t}{2} = 6$ ……….(2)

Solving equation (1),

⇒ s - t = 3

⇒ s = t + 3 ………..(3)

Substituting above value of s in equation (2), we get :

$\Rightarrow \dfrac{t + 3}{3} + \dfrac{t}{2} = 6 \\[1em] \Rightarrow \dfrac{2(t + 3) + 3t}{6} = 6 \\[1em] \Rightarrow \dfrac{2t + 6 + 3t}{6} = 6 \\[1em] \Rightarrow 5t + 6 = 36 \\[1em] \Rightarrow 5t = 30 \\[1em] \Rightarrow t = \dfrac{30}{5} \\[1em] \Rightarrow t = 6.$

Substituting value of t in equation (3), we get :

⇒ s = 6 + 3 = 9.

Hence, s = 9 and t = 6.