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An equation usually consists of a statement that holds the equality of two expressions. That means it’s a mathematical representation of two numbers or things that are equal and are placed on each side of an equals sign.

The microchips used in cars and dryers to the Internet present us with the right information; everything is related to equations. And solving equations is also a significant part of any student’s life unless you reach a level where you can choose the discipline you are interested in.

Some of you may seek help from professors, while others may use the best online accurate **equation solver** calculator with steps to solve the mathematical problems easily.

There are infinite equations out there. And no matter how difficult you find it hard to believe, but all the equations have integral roles to play in our daily lives. Sounds unbelievable?

Here are the three main equations in the mathematical world and their applications in the real world:

**Linear Equations**

The basic format of linear equations is:

ax + b= 0 where a is not zero and a is the slope. b is the point on which it cuts the y-axis.

In linear equations, you can simplify and operate each term in the equation to convert it into another equation of the same type. You may find the terms in this equation to be a product of a constant, a constant, or a single variable.

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**Example of linear equation with one variable **

15x – 80= 0

**Example of linear equations with two variables**

10x + 16y – 80= 0

Let’s say you want to solve this equation:

3x + 15 = x + 25

The ‘equals’ sign indicates a balance between both sides of the equation. It means if you alter one side of the equation, you must do the same to the other side. Keeping that in mind:

(3x – x) + 15 = 25

Subtracting 25 from both sides:

2x = 10

Dividing both sides by 2:

x = 5.

That was the basic information about linear equations and how to solve them. However, you may need online assignment assistance in case of complex equations. Now comes the most interesting part- the real-life applications of linear equations.

**Real-life Applications of Linear Equations **

**Rates**

Linear equations serve as the best tools when it comes to comparing rates of pay. For instance, let’s say one company has prepared to pay $450 a week and another company is prepared to pay $10 per hour.

And both the companies require you to work 40 hours every week. Now, how will you decide which company is profitable for your career? This is where the role of linear equations comes into play.

**Expression of the first company’s offer:**

450 = 40x

**Expression of the second company’s offer:**

y = 10 (40)

This is what you get after applying linear equations:

x = 11.25

That means you get a better rate of pay at $11.25 every hour from the first company.

**Variable costs**

Let’s say you want to take a taxi while being on vacation. Now the taxi charges $9 and another taxi charges $0.15 per mile for the same trip. You can use x to present the total number of miles needed to reach your destination and y to depict the overall cost of that ride. The linear equation would look something like this:

y = 0.15x + 9.

**Budgeting**

Let’s say you want to plan a party for an upcoming event. Wouldn’t you need to know how much it will cost to rent a space and make arrangements for the party? Linear equations can help you prepare a reasonable budget for any occasion.

For instance, if the rental space is $780 and the price for each person’s food is $9.75. So, the linear equation would look something like this:

y = 9.75x + 780

**Quadratic equations**

This one is a second-order equation. In quadratic equations, a variable will always consist of an exponent of 2 and the degree will always be 2. These equations will also always consist of two roots. There are certain types of equations known as biquadratic, which can be converted into quadratic equations.

Here’s the general format of quadratic equations:

ax^{2} + bx + c is not equal to zero.

Consider this example:

3x^{2 }= 48

Dividing both sides by 3, we get:

x^{2 }= 16

Square root on both sides provides us with:

x = 4.

Solving quadratic equations can be daunting initially. So, instead of wasting time, you can opt for assignment assistance online and learn how to solve these problems easily.

**Real-life Applications of Quadratic Equations **

**Calculating room areas**

It is quite common for people to calculate the area of their rooms, boxes, or land plots. Let’s say you want to build a rectangular box whose one side should be twice the length of the other side.

So, you need four squared pieces of wood to support the bottom of the box. You can use the ratio of both sides and create an equation to calculate the area of the box.

**Figuring a profit**

Quadratic equations play a great role in calculating business profits. You must decide how many products you need to produce to generate a profit in your business. Let’s say you want to figure out the price you should set for selling 12 glasses of lemonades. Use p as the variable in your equation.

So, the equation would look something like this: 12P – P^{2, }and this equation should be equal to the amount it took to produce 12 glasses of lemonade.

**Determining speed**

Did you know avid kayakers use quadratic equations to determine their speed while going up and down a river? Let’s assume a kayaker moves against the current at 15 km and the river moves at 2 km an hour. The total time he took to reach and return from the place is 3 hours. So, the quadratic equation would look something like this:

3 hours = 15 / (x – 2) + 15 / (x + 2) where x is the speed of the kayak.

**Simultaneous equations**

The equations are known as simultaneous equations because you need to solve all of them at the same time. You need algebraic skills to determine the values of letters within equations. If there is more than one unknown in the equation, it leads to an infinite number of solutions.

Consider this equation:

2x + y = 10

3x + y = 11

The coefficient of y is 1 in both equations. Subtracting both the equations leads to:

x = 3.

Substituting the value of x in any one of the equation gives us:

6 + y = 10

y = 4.

**Real-life Applications Of Simultaneous Equations **

**Rate, distance, and time**

Whether you want to calculate the best routes for cycling or running, simultaneous equations can help you with it. Consider the average speed and distance for different parts of the route to create a mathematical expression based on simultaneous equations.

**Planes, automobiles, and trains**

You must have come up with a formula for the examples mentioned above. So, you can use this formula to calculate the speed, time, and distances while traveling by train, plane or car.

**Deciding on a loan**

Simultaneous equations will help you decide which best loan is for you. You need to consider the interest rate, duration of the loan, and the monthly payment of the loan.

**Wrapping Up, **

Solving equations isn’t really fun. There are plenty of theorems to follow and one mistake can make all your hard work go down the drain.

But, as you can see, equations help you make some important decisions in your daily life. So, don’t fret the next time you are asked to solve some equations at school. Devote enough time to the task and get the hang of these equations and how to solve them.

**Also Read:** Top 5 tips for selling online courses

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