Solve the following system of simultaneous linear equations by the substitution method:

s - t = 3

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

Given,

s - t = 3 ……..(i)

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

From eqn. (i) we get,

s = 3 + t.

Substituting above value of s in eqn. (ii) we get,

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

∴ s = 3 + t = 3 + 6 = 9.

Hence, t = 6 and s = 9.