How Substitution Method works?

Substitution Method is the most easiest and straightforward technique to solve Linear equations in two variables. In this article, you'll learn how to use this method with the help of examples.

Linear equations in two variables is very important topics with examination point of view. There are three method with which we can solve the linear equations, namely, Substitution Method, Elimination Method and Cross Multiplication Method. You can definitely score good marks in examinations if you know how these techniques works.

As the name suggests, we have two variables in our linear equations and we marks both our equations as equation number 1 and equation number 2. We take one equation, say eq. no. 1 and express it in terms of x. Then we the expression equivalent to and substitute it in eq. no. 2. Now we solve this equation and obtain the value of y. Now that we have the value of variable y, we can again substitute value of y in the expression equivalent to x, to obtain the value of x. In this manner, we obtain the value of both the variables x and y. Simple, isn't it?

Just remember that the way we have expressed equation 1 in terms of x initially, you can express it in terms of y also and then proceed accordingly. Now let's take and example to understand how it works.

Let's say we have two equations :

x + y = 3 -------- eq 1
2x + 3y = 7 -------- eq 2

Now we take eq 1, and we express it in terms of x, and we'll have, x = 3 - y

We substitute the expression equivalent to x in eq 2, and we get,
2(3 - y) + 3y = 7
On solving we have, 6 - 2y + 3y = 7
Then, 6 + y = 7 => y = 7 - 6 = 1 => y = 1

Now we substitute value of y in expression equivalent to x,

x = 3 - y => x = 3 - 1 => x = 2

Therefore, solution to our linear equations is x = 2 and y = 1.

If you want to check more example refer this video Substitution Method

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