Question

Solve the following pair of linear equations by the substitution method
\[s - t = 3\] and \[\dfrac{s}{3} + \dfrac{t}{2} = 6\]
a). \[s = 2,t = 7\]
b). \[s = 9,t = 6\]
c). \[s = 3,t = 1\]
d). \[s = 6,t = - 9\]

Answer 1

Hint: To solve this question, we have to find the value of \[s\] in terms of \[t\] from equation one and put the value of \[s\] in equation second and then from that equation, we will find the value of \[t\] and substitute in one of the equation and find the value of another variable. This method is known as the substitution method.

Complete step-by-step solution:
Given,
Pair of linear equation \[s - t = 3\] and \[\dfrac{s}{3} + \dfrac{t}{2} = 6\]
To find,
The value of \[s\] and \[t\] from the pair of linear equations by substitution method.
Solving the first equation.
\[s - t = 3\] (given)
Taking \[t\] to the other side
\[s = 3 + t\] ……………………(i)
Now solving the second equation
\[\dfrac{s}{3} + \dfrac{t}{2} = 6\]
Taking LCM on denominator
\[\dfrac{{2s + 3t}}{6} = 6\]
On further solving
\[2s + 3t = 36\]
On putting the value of \[s\] from equation (i)\[s\]
\[2(3 + t) + 3t = 36\] (\[s = 3 + t\])
On further solving
\[6 + 2t + 3t = 36\]
On taking variables in one side and constant in other side
\[2t + 3t = 36 - 6\]
\[\Rightarrow 5t = 30\]
On taking \[5\] in another side of equal
\[t = \dfrac{{30}}{5}\]
\[\Rightarrow t = 6\]
Now put the value of \[t\] in equation (i)
Equation (i) is
\[s = 3 + t\]
\[\Rightarrow s = 3 + 6\]
\[\Rightarrow s = 9\]
The value of \[s\] and \[t\] satisfying the equation \[s - t = 3\] and \[\dfrac{s}{3} + \dfrac{t}{2} = 6\]
\[ \Rightarrow t = 6\] and
\[ \Rightarrow s = 9\]

Additional information:
Substitution method: Take one value from the equation (i) and substitute the value from equation (i) to equation (ii) and find the value of one variable and substitute that value in another variable. This method is known as the substitution method.

Note: To solve pair of linear equations in two variables first we have to take only one equation and then try to arrange one variable in terms of another variable and then substitute the value in equation second and then find the value of that variable and put that value in any of the equation in order to find the value of another variable.