# Introduction

**History**

First, the ancient mathematicians Aryabhata and Brahmagupta used algebraic notations. It is not the symbols which we are using now. After that, it has been developed by Brahmagupta. He developed modern multiplication, division, addition and subtraction based on Hindu-Arabic numerals. Then, they thought about how to find the value of unknowns.

In algebraic equations, we solve equations to obtain the value of one or more unknown. The word for "thing" or "object" in Arabic which was the main language of sciences during the Islamic civilization is "shei" which was translated into Greek as ‘xei’, and shortened to x, and is considered to be the reason for using x. It is also noted that "xenos" is the Greek word for unknown, stranger, guest, or foreigner, and that might explain the reasons why Europeans used the letter x to denote the "unknown" in algebraic equations

**Robert Recorde**

Robert Recorde was a Welsh physician and mathematician who introduced the "equals" sign (=) in 1557 in his book “The Whetstone of Witte”

Recorde's algebra text where two equal parallel line segments as the symbol for equality was used for the first time: "bicause noe 2 thynges can be moare equalle”

How variables are used in real life?

On your birthday, one of your friends gives a box of chocolates.

Another friend gives another box of chocolates as birthday gift.

So, now how many chocolates will you have?

Without opening the box, we cannot find the total number of chocolates. In these cases, we use variables for unknown number of chocolates. By solving the equation formed we can find the number of chocolates which is the unknown.

Let us have a quick review of what was studied in the previous classes.

# Equations

A mathematical statement that has two expressions separated by an equal sign is called an Equation. The expression on the left side of the equal sign has the same value as the expression on the right side.

A few examples of Equation

One or both of the expressions may contain variables.

When an equation contains only one variable it is said to be an equation in one variable

**Example : **7*x* + 4 = 5, 5* x*^{ 2} + *x* = 8.

If an equation contains only two variables it is an equation in two variables,

**Example : ***x* + *y*=8, *x*^{ 2} + 2* y*^{ 2} - 5* x* =0.

**Linear Equation**

If the highest power of the variable (x) in an equation is 1, it is said to be a linear equation.

**Example :**

*x*+ 4 = 5, 2

*x*+

*y*= 8.

In other words, linear equations involve only linear polynomials.

Sides of an Equation

Expression on the left hand side is known as LHS and on the right hand side is known as RHS of the equation. LHS and RHS are the sides of an equation.

**Solution of Equations **

The value of a variable which makes the equation true is called solution of the equation.

Consider the equation

Equation |
Value of the variable |
True/ False |

x + 3 = 12 |
2 | False |

5 | False | |

7 | False | |

8 | False | |

9 |
True |

Therefore, 9 is the solution of

*x*+ 3 = 12, since it makes the equation true.

Note that, other values are not solution of *x* + 3 = 12, since they do not satisfy the equation.