Question

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

• A. s = 8 and t = 5
• B. s = 9 and t = 6
• C. s = 12 and t = 10
• D. s = 5 and t = 7

Answer 1

The correct option is

B

s = 9 and t = 6

s - t = 3 ... (i)
$\frac{s}{3}+\frac{t}{2}=6$ ... (ii)
From equation (i), we get
s = t + 3
Substituting this value in equation (ii), we get
$\frac{t+3}{3}+\frac{t}{2}=6$
$\Rightarrow$ 2t + 6 + 3t = 36
$\Rightarrow$ 5t = 30
$\Rightarrow$ $t=\frac{30}{5}$ = 6
Substituting the value of t in equation (i),

$\Rightarrow$ s - 6 = 3

$\Rightarrow$ s = 3 + 6
We obtain, s = 9
$\therefore$ s = 9 and t = 6