Question

Solve :- 3x+5y=7 , 4x-y=2 by using Elimination method​

Answer 1

Elimination Method

Elimination Method is basically used to solve pair of linear equations to find the value of variables in equation.

In this method, we eliminate a variable from the equation to make it into one variable for the simplicity of getting solution. We can eliminate variables either by adding or subtracting both the equations.

But we have to make sure that the coefficients of similar variable is equal which can be done easily by multiplying or dividing whole equation by a constant term.

Let's see how this method words by solving given problem !

Given pair of equations :-

• $3x + 5y = 7 \bf . . . (1.)$
• $4x - y = 2 \bf . . . (2.)$

Multiply equation (2.) with 5

$\implies 5(4x - y) =5 (2)$

$\implies 20x - 5y =10 \bf . . . (3.)$

Now add equation (1.) and (3.)

${\implies(3x + 5y) + (20x - 5y) = 7 + 10}$

${\implies 3x + 5y + 20x - 5y= 17}$

${\implies 23x= 17}$

${\implies x= \dfrac{17}{23}}$

[ Here we have eliminated variable y to find the value of variable x ]

Now substitute this value of x in equation (1.) for finding the value of y.

$\implies 3x + 5y = 7$

$\implies \left (3 \times \dfrac{17}{23} \right)+ 5y = 7$

$\implies \left ( \dfrac{51}{23} \right)+ 5y = 7$

$\implies 5y = 7 - \dfrac{51}{23}$

$\implies 5y = \dfrac{161 - 51}{23}$

$\implies 5y = \dfrac{110}{23}$

$\implies y = \dfrac{110}{23 \times 5}$

$\implies y = \dfrac{22}{23}$

Hence we have obtained the value of x and y.