SOLVING LINEAR EQUATIONS BY ELIMINATION METHOD

Solving Linear Equations by Elimination Method :

Here we are going to see some example problems of solving linear equations in two variables using elimination method.

Question 1 :

Solve by the method of elimination

(i) 2x – y = 3; 3x + y = 7

Solution :

2x – y = 3  ----(1)

3x + y = 7 ------(2)

The coefficient of y in the 1st and 2nd equation are same.

(1) + (2)

         2x – y = 3

        3x + y = 7

       -------------

         5x   =  10

          x  =  10/5  =  2

By applying the value of x in (1), we get

2(2) - y  =  3

4 - y  =  3

y = 4 - 3 

y  =  1

Hence the solution is (2, 1).

(ii) x – y = 5; 3x + 2y = 25

Solution :

x – y = 5 -------(1)

3x + 2y = 25 ------(2)

The coefficient of y in the first equation is 1, the coefficient of y in the second equation is 2. So, we have to multiply the first equation by 2.

       2x - 2y  =  10

       3x + 2y  =  25

     -----------------

       5x  =  35

       x  =  35/5

      x  =  7

By applying the value of x in (1), we get

7 - y  =  5

y  =  7 - 5

y  =  2

Hence the solution is (7, 2).

(iii)  (x/10) + (y/5)  =  14 ; (x/8) + (y/6)  =  15

Solution :

(1) x 3 - (2)

(1) x 3  ==>  3x + 6y  =  420

                  3x + 4y  =  360

                (-)   (-)      (-)

                -----------------

                        2y  =  60

                        y  =  30

By applying the value of y in (1), w get

3x + 6(30)  =  420

3x + 180  =  420

3x  =  420 - 180

3x  =  240

x  =  240/3  =  80

Hence the solution is (80, 30).

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