A mathematically linear equation in two variables is a crucial idea that can be applied to several real-world scenarios. The concept of equations helps us gain a better understanding of the relationships between different variables, numbers, or objects.

From calculating monthly mortgage payments to determining the speed of a moving object, linear equations with two variables are used almost everywhere! We will dive deeper into these examples and explore more real-life scenarios where equations are used to solve problems.

In this post, you will find some practical instances of how linear equations in two variables are applied in real-world situations.

**Real-world applications of linear equations in two variables: examples and illustrations**

Here are a few illustrations of two-variable linear equations and how these equations are used in everyday life:

**1. Age difference between two people**

To determine the age difference between two people, we can use a linear equation. The equation is as follows:

**(x+d) – x = d**

Where d represents the age difference in years and x represents the age of one person. The other person’s age is represented as x+d. This equation shows that the age difference between the two people is equal to the difference in their ages.

**2. Speed and Time of person to travel a distance**

To calculate the distance covered by a person who travels using both walking and bus, we can use an equation that takes into account the speed and time of each mode of transportation. The equation is

**d = st + bt **

Where d is the distance covered in miles, s is the speed of walking in miles per hour, t is the time spent walking in hours, and b is the speed of the bus in miles per hour. This equation shows that the distance covered by the person is equal to the product of the speed and time spent walking plus the product of the speed and time spent on the bus. It’s a simple way to find out the distance covered by a person.

**3. To find the cost of something**

Let’s say, you need to find the best phone plan for your sim. The total cost of a phone plan is the sum of the monthly fee and the cost per minute for any additional minutes used. The total cost C for using x minutes is given by the equation

**C = 50 + 0.25x **

In this equation, we described the total cost C of a phone plan as a function of the number of minutes used x. The term 50 represents the fixed monthly fee of the plan, and the term 0.25x represents the cost of any additional minutes used.

**4. To determine earnings in a month **

An employee needs to find his monthly earnings, taking into account their hourly pay and any overtime compensation, here linear equation of two variables can be applied. Let’s take an example, The total of an employee’s hourly pay and any overtime compensation makes up their income from part-time work. The equation

**m = 15h + 20o**

Where m represents the employee’s total monthly earnings h represents the number of regular hours worked, and o represents the number of overtime hours worked.

**5. Money and Percentage**

Linear equations are also used in money matters in companies. For example**,** After adding a markup % to the price of the raw materials, a corporation calculates the cost of a product.

**C = R + (R * P)**

Where C is the final cost, R is the cost of the raw materials, and P is the markup %, which gives the final cost.

**6. Supply and Demand**

A linear equation can be used to model the relationship between the quantity of a good that is delivered and the price at which it is sold. For instance, if the supply of a specific good is described by the equation

**S = -2P + 20 **

then it follows that the amount supplied will fall by 2 units for every $1 increase in the good’s price.

**7. Calculating bank savings**

An individual has $1,000 in savings and receives a fixed interest rate of 5% annually. He wants to calculate his total saving. The linear equation that can be used to indicate the amount of money in the account after x number of years is as follows

**y = 1000(1 + 0.05)x **

Where x is the number of years and y is the total amount in the account.

**8. To find weight and height**

You can use a linear equation to determine how a person’s weight and height are related. For instance, you could plot data on a graph showing the heights and weights of a group of people and then apply a linear regression to fit a line to the data. The link between weight and height will be represented by the equation of this line.

**y = 0.5x + 20**

In this equation, y represents the weight, x represents the height, 0.5 is the slope of the line, and 20 is the y-intercept.

**9. Use in Engineering**

In engineering, the relationship between power, current, and voltage in an electrical circuit is described by Ohm’s Law, which states that the power P is equal to the current I times the voltage V. This relationship is written as a linear equation with two variables as

**P = IV**

where we can use it to find the power of an electrical object by multiplying current by its voltage.

**10. Use in physics**

To calculate the pressure of a gas in a container, we can use an equation that takes into account the weight and temperature of the gas. The equation is:

**P = kT/V + m*g/A**

where P represents the pressure of the gas in the container, T represents the temperature of the gas, V represents the volume of the gas, m represents the mass of the gas, g represents the acceleration due to gravity, A represents the surface area of the container, and k is a constant. This equation shows that the pressure of the gas is the result of the ratio between the constant, temperature, and volume plus the weight of the gas divided by the surface area of the container.

**How to make the concept more facile for kids?**

We can use simple tricks to teach and simplify the concept of linear equations to kids. Both teachers and parents can take help from it.

**1. Use real-life examples:**

Kids often find it easier to understand concepts when they can see how they are used in the real world. If children can relate things to their everyday experiences, they are more likely to comprehend and remember them. Make use of kid-friendly examples, such as those involving cost and quantity, supply and demand, or distance and speed.

**2. Use visual aids:**

Kids often learn better when they can see concepts demonstrated visually. Physical objects can be very helpful for helping kids understand math concepts. For example, you can use blocks or other objects to help kids understand how to solve linear equations. You can also use manipulatives like pattern blocks or counting bears to help kids understand it. Using these types of visual aids can help kids develop a better intuition for linear equations and make the concept easier to understand.

**3. Practice equations**

Keep providing kids with different examples and problems to work on, so they can build their understanding and confidence in solving linear equations. remember to make it fun and exciting. If you can make the learning experience enjoyable, kids will be more likely to engage with the concept and retain the information.

**4. Using technology**

Using a computer such as an interactive whiteboard, to make linear equations visualize and interact with kids. Kids tend to understand visuals better than oral or written, especially to explain mathematics concepts; using graphics, animation, and videos also be helpful to make concepts easy for them.

**Conclusion **

In conclusion, teaching children about linear equations with two variables and other kinds of equations like differential equations can be a challenging task, but with the right approach and methods, it can be made much more manageable. Using real-life examples, visual aids, and interactive activities can help children understand how linear equations work and how they apply them to their everyday lives. Additionally, it is important to use appropriate language and explanations that are tailored to the child’s age and understanding. Simplifying complex ideas can also make the topic more accessible to children.

An engineer, Maths expert, Online Tutor and animal rights activist. In more than 5+ years of my online teaching experience, I closely worked with many students struggling with dyscalculia and dyslexia. With the years passing, I learned that not much effort being put into the awareness of this learning disorder. Students with dyscalculia often misunderstood for having just a simple math fear. This is still an underresearched and understudied subject. I am also the founder of Smartynote -‘The notepad app for dyslexia’,