Real Life Example of Linear Equation in Two Variables

Linear equations in two variables are used to solve real-world problems involving two variables. One of the common real-life examples of linear equation in two variables is the problem of finding the cost of two or more items.

Problem Statement: A store sells pens and pencils. The cost of a pen is $5 and the cost of a pencil is $3. If a customer buys 4 pens and 6 pencils, what is the total cost?

Solution:

To solve this problem, we will use the following steps:

Step 1: Define the variables:

Let x be the number of pens.
Let y be the number of pencils.

Step 2: Formulate the equation:

The cost of 1 pen = $5
The cost of x pens = 5x

The cost of 1 pencil = $3
The cost of y pencils = 3y

Total Cost = 5x + 3y

Step 3: Substitute the given values:

x = 4 (because the customer buys 4 pens)
y = 6 (because the customer buys 6 pencils)

Total Cost = 5(4) + 3(6)
Total Cost = 20 + 18
Total Cost = $38

Step 4: Interpret the result:

The total cost of 4 pens and 6 pencils is $38.

Conclusion:

This is an example of a linear equation in two variables because it involves two variables (x and y) and the equation is linear (Total Cost = 5x + 3y). Linear equations in two variables are used to solve real-world problems involving two variables.

The concept of linear equation in two variables is used for calculating the overall marks in many examinations.If you are awarded 3 marks for a correct answer, -1 for an incorrectly answered question, and 0 for unattempted question,then the equation will be given as: 3x-y, where x refers to the number of questions answered correctly and y refers to the number of questions answere incorrectly.