# INTRODUCTION:-

In its previous blog, we learnt how to solve a pair of linear equation in two variables by substitution method. Now we will discuss the elimination method.

In the elimination method, we will eliminate any variable & find the values of variables.

## Elimination Method:-

In this method, we eliminate one variable from both equations & find the value of another variable in numeric form. Now put this value in any equation & find the value of a remaining variable.

Let's discuss by example...

### Question

**Solve the pair of linear equation in two variables.**

**2x-3y=5**

**3x-4y=2**

**Answer**

*We have a pair of the equation*

**2x-3y=5.......***Eq. 1***3x-4y=2.......***Eq. 2*

(

*For find the value of both variable we will eliminate anyone variable x or y. Here we are eliminating variable x).*

*(For this we take the coefficient of x from Eq.1 & multiply it to Eq.2. As it is we take the coefficient of x from Eq.2 & multiply it to Eq. 1. As shown below)*

**{2x-3y=5} × 3****{3x-4y=2} × 2**

**6x-9y=15****6x-8y=4**

*( Now we can eliminate variable of x & find the value of variable y)*

**6x-9y=15****6x-8y=4**__- + -____0 -1y=11__

*( In the above solution, for elimination we are changing equation signs & solved it)*

**-1y=11****y = 11÷(-1)****y = (-11)........***Eq.3*

*( Now put the value of y(Eq. 3) in Eq.1 for finding the value of x. We may put it in Eq.2 also)*

**2x-3y=5****2x-3(-11)=5****2x+33=5****2x=5-33****2x=-28****x=-28÷2****x=-14**

**Finally we get the values of variable x=(-14) & y=(-11).**

**CONCLUSION:-**

Here we get a solution for linear equation in two variables by the elimination method. In the next blog, we will discuss the cross multiplication method & will find the values of variables.