**What is Linear Equation?**

A **linear equation** is an algebraic equation in which the highest exponent of the variable is one. Linear equation has one, two or three variables but not every linear system with 03 equations. Usually, a system of linear equation has only a **single solution** but sometimes, it has **no solution** or **infinite number of solutions**.

A two variables linear equation describes a relationship in which the value of one variable say ‘x’ depend on the value of the other variable say ‘y’. If there are two variables, the graph of a linear equation will be straight line.

**Standard Form of Linear Equation**

Linear Equations have a standard form like:

*Ax + By = C*

Here, A, B, and C are coefficients, whereas, x and y are variables.

General form of the linear equation with two variables is:

**y = mx + c, m **≠** 0**

## Linear Equation Formula

Some general formulas are:

- Slop Intercept Form :
- Point Form:
- Two Point Form:

**Examples of Linear Equations**

In above examples, the highest exponent of the variable is 1.

**Equation with one Variable:**An equation having one variable, e.g.- 12x – 10 = 0
- 12x = 10
**Equation with two Variables:**An equation having two variables, e.g.- 12x +10y – 10 = 0
- 12x +23y = 20
**Equation with three Variables:**An equation having three variables, e.g.- 12x +10y -3z – 10 = 0
- 12x +23y – 12z = 20

### Solved Examples of Linear Equations:

**Example
No.1:**

**Solution:**

**Example
No.2:**

**Solution:**

**Example
No.3:**

**Solution:**

In linear equation, the sign of equality (=) divides the equation into two sides such as L.H.S. and R.H.S.

**Solution of linear equation**

In the given equation, the value of the variable which makes L.H.S = R.H.S is called the solution of linear equation.

**Examples
No.1**

x +
6 = 8 is a linear equation.

Here, L.H.S. is x + 6 and R.H.S. is 8

If we put x = 2, then left hand side will be 2 + 6 which is equal to right hand
side

Thus, the solution of the given linear equation will be x = 2

**Example
No.2 **

3x
– 2 = 2x – 3 is a linear equation

If we put x = -1, then left hand side will be 3(-1) – 2 and right hand side
will be 2(-1) – 3

We obtained,

-3 – 2= -2 – 3

-5 =
-5

Therefore, L.H.S. = R.H.S.

So, x = -1 is the solution of given linear equation.

**Types of Linear Equation: **

There are three types of linear equations

- Conditional Equation
- Identity Equation
- Contradiction Equation

**1. Conditional Equation:**

Conditional equation has only one solution. For example,

**2. Identity Equation:**

An identity equation is always true and every real number is a solution of it, therefore, it has infinite solutions. The solution of a linear equation which has identity is usually expressed as

Sometimes, left hand side is equal to the right hand side (probably we obtain 0=0), therefore, we can easily find out that this equation is an identity. For example,

**3. Contradiction Equation:**

A Contradiction equation is always false and has no solution. Contradiction equation is mostly expressed as:

For example,

**Linear Equations represent lines**

An equation represents a line on a graph and we have required two points to draw a line through those points. On a graph, ‘x’ and ‘y’ variables show the ‘x’ and ‘y’ coordinates of a graph. If we put a value for ‘x’ then we can easily calculate the corresponding value of ‘y’ and those two values will show a point on a graph. Similarly, if we keep putting the value of ‘x’ and ‘y’ in the given linear equation, we can obtain a straight line on the graph.

**Graphical representation of Linear Equation**

we can put the values of ‘x’ and ‘y’ into the equation in order to graph a linear equation. We can use the “intercept” points. Few below mentioned points must be follow:

- Put x = 0 into the equation and solve for y and plot the point (0,y) on the y-axis
- Put y = 0 into the equation and solve for x and plot the point (x,0) on the x-axis
- Finally, draw a straight line between the two points

**Check
your skills to find the solutions of these linear equations:**

**See Also : ****Types of Mathematical Equations**