A linear equation is an equation in which there are either one or two variables, the power (exponent) on each variable being only 1 (that's why it is called linear). No term in the equation contains the variable/s in the denominator. If there are two variables in a linear equation, the two variables are never multiplied together in a single term (because that would give the equation a degree of 2).

There are two types of linear equations:

There are two types of linear equations:

- Linear equations containing one variable
- Linear equations containing two variables

### Identifying linear equations

After simplifying an equation, you can identify whether it is linear or not by the following rules:

- There is either one or two variables in the equation
- No variable is in the denominator of a fraction
- No variable has a power (exponent) other than 1
- If there are two variables, they are not present together in a single term

For example,

- `2x^2 - 1 = 0` is not a linear equation since the power on 'x' is 2
- `x^3 + 3x^2 + 4x + 2 = 0` is not a linear equation since 'x' has a power of 3 and 2.
- `3/x + 4 = 5x` is not a linear equation since 'x' is in the denominator.
- `3xy + 4x = 6y` is not a linear equation since 'x' and 'y' are multiplied together in the first term.

On the other hand,

- `x + y = 1` is a linear equation
- `2x + 4 = 1`
- `3/x + 2 = 1` is a linear equation because on simplifying, we get `3 + 2x = x` which has no 'x' in the denominator or a power greater than 1.

### LHS and RHS of a linear equation

A linear equation always has a = sign. The expression on the left of the = sign in an equation is called the LHS (Left Hand Side) and the expression on the right of the = sign is called the RHS (Right Hand Side).

For example, in the following equation,

the expression on the left of the = sign is 2x + 4 and hence it is the LHS, whereas the expression on the right of the = sign is 5x + 3 and is called the RHS.2x + 4 = 5x + 3

## No comments:

## Post a Comment