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What is a Linear Equation?

Linear Equation

In mathematics, there are various types of equations, likewise, an equation that has the highest power of ‘1’ for the variable can be defined as the linear equation. This type of equation is also defined as the one-degree equation. The rationalized form of a linear equation is in the form of ‘ax + by + c = 0’. Here, the letters ‘a’,’b’, and ‘c’ are defined as the constants whereas ‘x’ and ‘y’ are denoted as the variable. Some examples of these equations are as follows: 2x + 3, 3x + 2, x = 8y – 9, y – x = 9 and so on. The graph when plotted for a linear equation always results in the formation of a straight line, i.e. horizontal line or vertical line. In this article, we will try to cover some basic concepts regarding linear equations such as: how to solve a linear equation, some calculations, and do a brief analysis about it. 

How to Solve an Equation?

The process of finding or calculating the unknown value of a particular variable i.e. ‘x’, ‘y’ and ‘z’ is known as solving an equation. There are various ways through which you can solve an equation. Some of them are as follows: trial and error method, using the method of factorization, the process of balancing an equation, the method of transposing, and many more. An equation is always the same if the values of the left-hand side and right-hand side are interchanged. As mentioned, there are various ways of solving an equation, but for different equations such as linear equations, radical equations, quadratic equations, and so on. In the next few sections, we will decode this equation and do some examples related to it. 

Methods of Solving a Linear Equation

As mentioned above, an equation that has the highest power of ‘1’ for the variable can be defined as the Linear equation. In the next paragraph, we will deal with the methods of solving a linear equation. The following points below analyze the methods:

  1. In order to solve an equation, weighing both sides of the equation is very important i.e. ( LHS = RHS). 
  2. The standard form of a linear equation is, ax + by + c = 0. We should try to bring the variables ( x,y ) on one side and on the other side the constants ( a,b, and c ). 
  3. The last method is to find the value of the unknown variable and get the appropriate answer. 
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Let us try to solve some examples related to the linear equation so that the concept becomes clearer to you. 

Example 1: Find the value of ‘x’ if the given equation is 4x + 2 = 6 

Given that, 

Equation = 4x + 2 = 6,

Now, 4x = 6 – 2 ( as 2 moves to the other side, thus a negative sign is used.)

4x = 4,

X = 4/4 = 1 

Therefore, the value of x for the given equation is equivalent to 1. 

Example 2: Find the value of ‘y’ if the given equation is 2y + 4 = 6 

Given that, 

Equation = 2y + 4 = 6,

Now, 2y = 6 – 4 ( as 4 moves to the other side, thus a negative sign is used.)

2y = 2,

y = 2/2 = 1 

Therefore, the value of y for the given equation is equivalent to 1. 

Some Calculations Based on Solving an Equation

Example 1: Find the value of the ‘z’ if the equation is, 4y = 20 using the method of transposing?

Given that, 4y = 20 

Using transposing method, y = 20 /4,

Y = 5. 

Example 2: Find the value of ‘x’ if equation is equivalent to, 2x + 3 = 17.

Given that, 

Equation =  2x + 3 = 17.

Now, 2x + 3 – 17 = 0.

2x + 3 – 3 = 17 – 3 ( adding both the sides 3 )

X = 7 ( when calculated).

If you want to learn about linear equations, visit Cuemath.