Question

Solve the pair of linear equations by the substitution method.
$s - t = 0$
$\dfrac{s}{3} + \dfrac{t}{2} = 5$

Answer 1

Hint – In this question take out one variable in terms of other variable from any of the two given equations and then substitute it in other equation, this helps formulation of an equation which is solemnly in one variable, solve it to get the variable, then use this value obtained to get other variable.

Complete step-by-step answer:
Given linear equations are
$s - t = 0$..................... (1)
$\dfrac{s}{3} + \dfrac{t}{2} = 5$................... (2)
Now we have to solve this linear equation by substitution method therefore,
From equation (1) we have,
$ \Rightarrow s = t$................. (3)
Now substitute this value in equation (2) we have,
$ \Rightarrow \dfrac{t}{3} + \dfrac{t}{2} = 5$
Now simplify this equation we have,
$ \Rightarrow t\left( {\dfrac{{2 + 3}}{6}} \right) = 5$
$ \Rightarrow t\left( {\dfrac{5}{6}} \right) = 5$
$ \Rightarrow t = 6$
Now from equation (3) we have,
$ \Rightarrow s = t = 6$
So (s, t) = (6, 6)
Hence this is the required solution for the given pair of linear equations.

Note – This question primarily focuses on solving by method of substitution but however there can be another method to solve problems involving two linear equations in two variables. It is elimination, in this method the coefficients of a specific variable of both the equations are made the same and then eliminated using basic operations of addition or subtraction. The other variable which is non-eliminated is taken out. The eliminated variable can be taken out using this variable obtained.