Linear Equation

Linear Equation

An equation in which the highest power of the variable involved is 1 is called a linear equations.The linear equation which has only one variable in it is called linear equations in one variable.

Solution of An Equation

A number which makes LHS and RHS equal when it is substituted for the variable in an equation is said to satisfy the equation and is called a solution of root of the equations.

Rules for solving an Equations

1. We can add the same number to both the sides of an equation.
2. We can subtract the same number from both the sides of an equation.
3. We can multiply both the sides of an equations by the same non zero number.
4. We can divide both the sides of an equation by the same non zero number.

Transposition

Any term of an equation may be taken from one side to the other side with a change in its sign, this does not affect the equality of the equation and this process is called transposition.

Consider an equation x + 8 = 3

We can write it as

x + 8 – 8 = 3 – 8

Similarly

x – 7 = 2

⇒ x – 7 + 7 = 2 + 7

⇒ x = 2 + 7

Applications of Equations

As we learnt how to change the word statements in the form of an equation. In the same manner, we can translate the word problems (on numbers, relating to age, area, speed, etc) in the form of an equation and then solve it.