ELIMINATION METHOD: Pair of linear equation in two variables

UTPAL SHARMA

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.



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