How Elimination Method work

Elimination method is my second most favorite method to solve a pair of linear equations in two variables. In this article, we’ll understand the process of how to use Elimination method.

As discussed in the earlier article, we know the three methods to solve linear equations in two variables are Substitution Method, Elimination Method and Cross Multiplication Method. There are times when Elimination method will be most handy and will get the results faster then Substitution Method. Let’s dive right in, shall we?

You take one of the two equations and apply some transformation (that is multiply or divide the equation with some number) in order to make one of the x or y terms equal to the x or y term on second equation. Now that we have same x or y terms, subtract the resultant equation from equation number 2, in that way, on solving you’ll get the value of one variable (x or y). Then, put the value of variable you just got, into one of the original equations and solve for other variable. Now, you have the value of both the variables as the solution. Simple, isn’t it?

Let’s understand this method with one example. We have pair of linear equations –

2x + 3y = 8 —–> eq 1

x + 2y = 6 —–> eq 2

Please observe that if we multiply eq 2 with 2, we will have x term as 2x (equivalent to x term in eq 1). So, we multiply eq 2 with number 2, and we get

2x + 4y = 12 —–> eq 3

We mark it as eq 3. Now as have same x terms, we subtract equation 1(Minuend) from equation 3(subtrahend). While subtracting, we invert the sign of terms of equation being subtracted. So we have,

(2x + 4y = 12) – (2x + 3y = 8) => (y = 4)

Now we have y = 4. we put this value in eq 2 and solve it for x.

x + 2y = 6 => x + 2(4) = 6 => x + 8 = 6

=> x = 6 – 8 => x = – 2

Therefore, x = – 2, y = 4 is the solution to our given pair of linear equations.

I hope the method is clear to you. Still if you want to refer more solved examples. Check out Elimination Method video. You’ll find more videos on this Topic there on Happy Learning.

If you still have doubts, feel free to connect or leave your query in comments. Don’t forget to Subscribe Happy Learning for more videos. Thank you.