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Linear Equations

An overview of what linear equations are and their significance along with how such mathematical problems can be easily solved.

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Mathematics is an integral part of science. Therefore, just like science, mathematics is an essential part of our daily life as well. We may fail to notice, but mathematics plays a very crucial role in our day-to-day mundane life. A linear equation is an element of mathematics that plays a significant role in the advanced level of mathematics as well. Complex classes of equations are made based on linear equations.

What are linear equations?

A linear equation is an equation based on algebra. In a linear equation, each term comprises an exponent of 1. After the equation is presented on a graph, the equation constantly forms a straight line. It is also the reason why it is known as a ‘linear equation.’ It is an equation where the maximum power of one variable cannot exceed 1. Therefore, it is called a one-degree equation. There is nothing called linear equation formula, and it just has a basic standard according to which every equation is presented. Ax + B = 0 is the standard form according to which every linear equation is given. Any change in the state will not qualify as a linear equation. In Ax + B = 0, x signifies a variable, the coefficient is denoted as A, and B is constant. However, there is another form that does qualify as a linear equation. In this form, there are two different variables, and it is known as a two-variable equation. The standard form of two variable linear equations is Ax + By = C. In this case, x denotes one variable, and y represents another variable. Coefficients in the equation are A and B, and C is the constant.

Use of linear equations in real life

Linear equations have a lot of implications in real-life scenarios. In a linear equation, one variable is dependent on another one. In real life, the linear equation can be used in almost every situation where an unprecedented quantity can be depicted by a linear equation: for instance, figuring out the level of income over a period, calculation of the rates of mileage, or estimating profits. Numerous people use linear equations in daily life. They may not notice it, but calculations done in the mind also count as linear equations. Following are some linear equation examples concerning some commonly faced real-life problems.

Variable Costs

Think about taking a cab during a trip to your vacation house. You get to know that the cab service is 90 rupees to pick up your family from your home and bills another 50 rupees per kilometer. Even by not knowing how much distance needs to be covered to reach the destination, you can use a linear equation to find the charge of any cab ride you take. Taking ‘x’ as the distance in kilometers and ‘y’ as the charge of the cab ride, the equation will be y = 50x + 90.

Rates

To compare rates of payments that ought to be made, the linear equation can prove to be an effective tool. For instance, if a company is willing to pay two thousand rupees every week and another organization is willing to pay fifty rupees hourly, where both of them want you to work for a total of 40 hours weekly, which company should you choose? In this kind of situation, the linear equation proves to be handy. The offer made by the first company can be expressed as 2000 = 40x. Likewise, the request made by the second company can be represented as y = 50(40). Now, after calculating and comparing both the offers, you will find that the request made by the former company was better than the second one.

Conclusion

A linear equation is such an essential part of mathematics that it is used widely in almost every aspect of mathematics. The use of linear equations is not limited to mathematics. In any situation where any kind of prediction or decision has to be taken, a linear equation is applied. Linear equations can often be confused as linear functions, but they are not the same. All linear equations are linear functions, but all linear functions are not linear equations. Linear equations always make a straight line when traced on a graph. Therefore, to make accurate estimations or to make accurate decisions, proper understanding and correct application of linear equations are necessary.

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