Let us solve the following linear simultaneous equations in two variables by the method of elimination:

Let us take as and

Then above equations can be written as

14a + 3b = 5 (i)

21a - b = 2 (ii)

In this problem, we will eliminate ‘b’ from both the equations.

Multiplying equation (ii) with 3, we have

⇒

Putting the value of a in equation(i) gives b = 1

Now Since and It will form again a system of linear equations in x and y.

Rearranging the above equation

x + y = 7 (iii)

x – y = 1 (iv)

⇒ x = 4, putting the value of x in equation(iii) gives y = 3.

Hence the solution of the linear equation is x = and y = 3.