Question

# Solve the following pair of linear equations by Substitution method:2x - 3y = 19 and 3x - 2y = 21

Hint: The substitution method is the algebraic method to solve simultaneous linear equations. As the word says, in this method, the value of one variable from one equation is substituted in the other equation. In this way, a pair of the linear equations gets transformed into one linear equation with only one variable, which can then easily be solved.

As the given equations are 2x - 3y = 19 and 3x - 2y = 21

So, let 2x - 3y = 19 -(Eq 1)

And 3x - 2y = 21 -(Eq 2)

As, given in the question that we have to solve the two equations by substitution method,

So, we cannot use any other method.

So, now we substitute value of y from 1 equation to y of equation 2

So, finding value of y from equation 1 we get,

3y = 2x - 19

On solving above equation we get,

y = $\dfrac{{2x - 19}}{3}{\text{ (3)}}$

So, now putting value of y from equation 3 to equation 2

Now, equation 2 becomes,

$\Rightarrow 3x - 2\left( {\dfrac{{2x - 19}}{3}{\text{ }}} \right) = 21$

Solving above equation by taking LCM on LHS of the equation we get,

\Rightarrow $\dfrac{{9x - 4x + 38}}{3} = 21$

Cross - multiplying and solving above equation it becomes,

$\Rightarrow 5x = 63 - 38 = 25$

$\Rightarrow {\text{So, }}x = 5$

putting value of x in equation 3 we get value of y

$\Rightarrow y = \dfrac{{2*5 - 19}}{2} = - 3$

Hence x = 5 and y = - 3

NOTE: - Whenever you come up with this type of problem where the method to solve the equation is specified then only use that method only and if not specified then we can use any method to solve equations.