Before you we try to understand the system of linear equations, we must understand the basic terminologies that we are going to use in the linear algebra.

### Linear Equations

Linear equation represents a straight line on a xy-plane or co-ordinate plane.

- The are
**real number constants**and both cannot be zero at the same time. - The and are called
**variables**. Hence, the equation is linear equation in variable x and y.

Therefore, linear equation in n variable is given as

where and are real number constants.

#### Examples of linear equations

Here are some examples of linear equations.

```
```

From the above examples, note that linear equations show following characteristics.

- There is not term in the equation with root or product.
- All variables are in power of 1.
- They do not appear as an argument of another function.

Here are examples of non-linear equations to help you understand the basic differences.

```
```

### Solution Of Linear Equations

A linear equation

` `

has a sequence of numbers

` `

as **solution **which satisfy the equation once we substitute them with the variables.

For example,

```
The solution is
Then,
will satisfy the equation.
```

The set of all solutions of a linear equation is called** solution set or general solution** to the linear equation.

#### How to find solution to linear equations ?

Now we will solve two linear equation using substitute method.

```
Problem #1 : solve
-------------------------------------------
Solution:
----------
We can solve like ordinary algebraic equation. Solve for x for solve for y.
Add to both side of the equation
now we have
Let's give an arbitrary value to y. This way we get value for x.
Therefore,
Problem #2 : solve
------------------------------------------------------------
Solution:
---------
This time we can solve for two variables and get the third. We get following equations.
Let us give arbitrary value to and .
```

### System of Linear Equations

The **system of linear equations** is a set of linear equations with variables , …,.

```
```

The solution set , …, when replaced with variables , …,

will satisfy every equation in the **linear system.** In the above system of linear equations,

and

will satisfy all the equations.

In the next post, we will discuss about **inconsistent **and **consistent **system of linear equations.