An equation is a mathematical statement that contains an equal to the “=” symbol. Linear equations are one-degree equations. A linear equation is an equation written for two distinct variables. This equation will be a linear combination of these two variables, with the possibility of a constant. Surprisingly, when it is plotted on a graph, the result is always a straight line – hence the name linear equations.
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Linear Equations: How Do You Solve Them?
You should have a good understanding of linear equations and their various forms by now. Solving an equation is not a very big task! Let us now look at examples of how to solve linear equations or line equations in one variable, two variables, and three variables. Here are step-by-step instructions for solving these equations.
- Addition/Subtraction: Add or subtract the same number on both L.H.S and R.H.S of the equation.
- Multiplication – Take the same number and multiply on both sides of the equation.
- Division – Divide both L.H.S and R.H.S with a common number.
- Apart from these, you can also try expanding, factorizing, squaring to solve a linear equation.
When solving an equation that is linear and both sides of the linear equation must be balanced. The equality sign indicates that the expressions on either side of the ‘equal to’ sign are the same.
Linear Equation Examples
A linear equation can be written in various ways. If it follows a certain set of rules, any simple equation in x and y can be called a linear equation. For example, in the equation, the highest (and only) degree of both x and y variables should be 1. Aside from that, constants (zero degree variables) can be present.
Understanding of Linear Equation
Linear Equations encompass a wide range of equations. It is with one variable, linear equations with two variables, and so on. One constant remains in every equation: the highest (and only) degree of all variables in the equation should be 1. Aside from that, constants (zero degree variables) can be present. Let’s take a look at the “Mind Reader” game, which will assist you in better understanding linear equations.
Appu created the game “Mind Reader.” He would like to play it with his friends. So he asks one of his friends, Kaira, to come up with a number, multiply it by two, and subtract five from it. He then inquires about the final outcome. Kaira says, “It is 13,” and Appu immediately says that the number Kaira initially thought of was 9. Kaira nods, and Appu’s friends, including Kaira, are taken aback! Everyone is curious about how the game “Mind Reader” works. Do you understand how it works? You will understand how it works by the end of this brief lesson. If you want to learn the fundamentals of it, you can log in to cuemath.com.
Graph of a Linear Equation
It is in one variable x produces a vertical line parallel to the y-axis, whereas a linear equation in two variables x and y produces a straight line. The geometrical representation of a degree one equation is a straight line, which is why it is called a linear equation.
Applications of Linear Equation
Some common real-world applications of linear equations include the computation of:
- Age-related issues
- Problems with speed, time, and distance
- Geometry issues
- Money and the proportion of problems
- Wage and hourly rate issues
- Force and pressure issues
It can be used to represent almost any situation in which an unknown quantity exists, such as calculating income over time, calculating mileage rates, or predicting profit. Many people use it on a daily basis, even if they do the calculations in their heads rather than drawing a line graph.
Key Takeaways
- The values of the variable that make a linear equation true are referred to as the linear equation’s solution or root.
- If the same number is added, subtracted, multiplied, or divided into both sides of it, the solution remains unchanged.
- A straight line is the graph of it with one or two variables.
