Solve the following pair of linear equations by the substitution method.
$s-t=3$
$\frac{s}{3}+\frac{t}{2}=6$

(S=9, T=6) $s-t=3$ $...(1)$
$\frac{s}{3}+\frac{t}{2}=6$ $...(2)$
From equation $(1)$,we express $s$ in terms of $t$:
$s = t + 3$ $...(3)$
Substituting the value of $s$ from equation $(3)$ into equation $(2)$:
$\frac{t+3}{3} + \frac{t}{2} = 6$
Multiply the entire equation by $6$ (the $LCM$ of $3$ and $2$) to clear the denominators:
$2(t+3) + 3t = 36$
$2t + 6 + 3t = 36$
$5t + 6 = 36$
$5t = 30$
$t = 6$ $...(4)$
Now,substitute the value of $t = 6$ into equation $(3)$:
$s = 6 + 3$
$s = 9$
Therefore,the solution is $s = 9$ and $t = 6$.