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Linear Equation with two variables by Substitution Method

Linear Equations in Two Variables by Substitution Method

Dear Readers,

Although there are a multiple method to solve linear equations with two variables (like substitution method, elimination method, graphical method & matrix method). But in this article we will limit ourselves to substitution method. While other methods, we will be discussing in our subsequent articles.

(Don’t forget to take the quiz at the end of this article)

Let’s understand the concept with the help of an example:

Suppose we have a linear equation in two variables as

2X + 3Y = 6

If you look at the equation carefully, you will find that there are two variables X & Y in the equation. The degree or power of X & Y is unity and the variables are not multiplied with each other. Therefore, we can call this as Linear equation in two variables.

As you can see that the above equation has two variables X & Y. So, to arrive at the values of X & Y we need one more equation having the same variables.

Solving Linear Equations with Two Variables – Substitution Method (Definition)

Before delving into the steps to solve the problem, let’s understand the meaning of  the word ‘Substitution’

Substitution refers to the act of replacing one thing with another. From the meaning itself, you will get an idea that substitution method involves some sort of replacement. Basically, in this method we will represent one variable in terms of other variable after that substituting this value into the other equation.

Steps to Solve Problems- Substitution Method

2X + 3Y = 6 ————–(1)

6X + 4Y = 13 ————–(2)

Step 1: Solve any one of the equation and represent any variable either X or Y in terms of other variable.

So, solving equation (1) and representing X in terms of Y.

2X + 3Y = 6

2X = 6 ― 3Y

X = 3 ― 3Y/2  ————(3)

Step 2: Now substituting the value of one of the variable (which has been represented in terms of other variable) into the other equation. This will result in one equation with one variable that we can easily solve.

In this case, substituting the value of X in equation (2) we get,

6 (3 ― 3Y/2) + 4Y = 13

18 – 9Y + 4Y = 13

5Y = 5

Y = 1

Step 3: Once we have arrived at the value of one of the variable then substitute this value to any one of the equation to get the value of the other variable.

Substituting the value of Y in equation (1) we get,

2X + 3×1 = 6

X = 3/2

Solution is ( 3/2 , 1)

Note: If you want to cross-check just put the value of X & Y in the above equation (1) & (2) to see whether L.H.S = R.H.S or not. And, if left-hand side value is equal to the right-hand side then the above obtained solution is correct.

Linear Equations with two variables - Quiz

Read the instructions carefully:

  • Total number of questions = 5
  • For each correct answer 3 marks will be awarded.
  • There is no negative marking.
  • Time allotted – 7 minutes. 

Leaderboard: Linear Equations with two variables - Quiz

maximum of 15 points
Pos. Name Entered on Points Result
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