The term “linear equation” takes its origin from the connection between lines and equations. Linear equations are composed of one or two variables, and one variable is reliant on the other variable. A linear equation in one variable is an equation with one variable which has only one solution. Linear equations in two variable have two solutions, and their solutions form a line. The equations are helpful to illustrate the relationship between two variables.

Nearly in any situation in which there is an unknown quantity, we can use a linear equation to figure out the results, for example, calculating earnings over the course of time, estimating the performance rates, predicting profits, etc. These linear equations are widely used in everyday calculations without us even realizing it. Although we don’t draw a graph line to represent them, we still perform them in our heads. For instance, while estimating the amount to be paid for a taxi ride depending on the miles being traveled.

## What are Linear Equations?

A linear equation is an algebraic equation that comprises one or more than one variable, equating sign, and a minimum of two expressions. Linear equations are the most basic form of algebraic equations; working with exponents or square roots is not required to solve these equations. When graphed on a coordinate grid, a linear equation always generates a straight line. A common form of a linear equation is p = mq + b; however, equations such as 2x = 14, .7 – t = 9 and 980 = 200 + 18x are also linear equations.

## How to Solve Linear Equations?

Solving linear equations is the foundational skill for any algebra student to learn. Solving these equations provides the student with the basic understanding to solve any complex algebraic equation. Thus for algebra students being skillful in solving linear equations is a very important skill to have. The students can practice solving linear equations over and over to master this skill. Here are some of the steps which a student can follow to solve any linear equation.

• The first and foremost step involved in solving linear equations is to simplify each side of the equation as much as possible. Students can use the distributive property to remove the parentheses and any grouping symbols from the equation.
• The second step in solving the linear equations is to combine all like terms. By putting all the variables on one side of the equation, students can apply the addition or subtraction property to combine these terms.
• Get all the constant terms on the other side of the equation. Use the Addition or Subtraction Property of Equality.
• The next step is to find the value of the variable– by making use of the multiplication and division property to make the coefficient equal to 1 of the equation, students can find the value of the variable in a linear equation.
• Once the value of the variable is determined, validate the solved equation by substituting the solution into the original equation and verifying that the result of the equation is true for any value of the variable. 