# Solving An Equation ## Introduction

To find the solution of an equation, we need to determine the values of the variable that makes the given equation a true statement. Solving an equation is similar to finding out the answer to a puzzle. Any number that makes the equation true is termed the solution of an equation. Hence, it is termed as the answer to a puzzle.

## What Is An Equation?

An equation represented by the symbol (=) says that two things are equal. It is represented as

(y – 2) = 4

In other words, it says that what is given on the left side (y – 2) is equal to the right side (4).

Hence, the equation is similar to a statement that says “this equals that”.

## What Is Solving An Equation?

A solution to an equation is the value of a variable that makes the statement true when substituted into an equation. Therefore, the process of determining a solution to an equation is known as solving the equation.

## How To Determine Whether Number Is A Solution To An Equation?

Following are the steps to determine whether the number is a solution to an equation:

• The first step is to substitute the variable’s value in the given equation.
• The second step is to solve the expression on both sides of the equation.
• The third step is to find out whether the resulting equation is true or not.

If the resulting equation is true, the number is a solution.

If the resulting equation is not true, the number is not a solution.

Example: Find the solution for an equation x + 6 = 11

Solution:

Substituting 5 for x in x + 6 = 11 gives

5 + 6 = 11

11 = 11

LHS = RHS

The number “5” equals both sides of an equation.

Hence, 5 is the solution of a given equation.

# Linear Equations

## Introduction

A linear equation is an equation whose each term is linear (i.e, the product of a variable and the first power of a variable) or constant (simply the real number). In other words, a linear equation is an algebraic equation through which a straight line is formed when an equation is graphed. Each term in the linear equation is either a constant, a product of a constant, or a single variable. This topic can be understood in a fun way from Cuemath.

## What is Known as Linear Equation?

A linear equation, also known as a one-degree equation whose greatest power of the variable is always 1. For example:

• y = 7x – 6
• y + 2x -1 = 0

## Linear Equation in One Variable

A linear equation in one variable is expressed in the form of Ax + B = 0, where “x” is the variable and a and b are the constant in the equation. In a linear equation in one variable, the constants a and b should be non-zero real numbers.

Examples:

• 4x + 3 = 15
• 3y + 43 = 8
• 2z + 15 = 82

## How To Solve Linear Equations In One Variable?

Following are the steps to solve linear equation in one variable:

1. Observe the given linear equation carefully.
2. Determine the quantity you need to find out.
3. Split the equation into two parts i.e. LHS and RHS.
4. Now find out the terms containing constants and variables.
5. Transfer all the constants on the RHS of the equation and variables on the LHS of the equation.
6. To find the value of the variable, perform algebraic operations on both sides of the equation.

Example: Solve x + 12 = 18

Solutions:

Let us first transfer constants and variables on the LHS and RHS respectively:

x + 12 = 18

x = 18 – 12

x = 6

The value of x is 6.

## Linear Equation In Two Variables

A linear equation in two variables is expressed in the form of Ax + By + C = 0. Here a, b, and c are real numbers and a and b are non-zero. For example:

• x + y = 150
• 2x + 3y = 4.5

## How To Solve Linear Equations In Two Variables?

There are three methods to solve linear equations in two variables. These are:

• Graphing Method
• Substitution Method
• Elimination Method

Example: Find the solution of the following linear equation in two variables:

2a + 3b = 12

Considering a = 3 and b = 3, we get

2a + 3b = 2(3) + 3(2) = 12

12 = 12

This solution can be written in an ordered pair like (3,2). First, write the value of a and then write the value of b.

Hence, (3,2) is the solution of a given linear equation in two variables.