A** system of linear equations** means two or more linear equations. (In plain speak: 'two or more lines') If these two linear equations intersect, that point of intersection is called the **solution** to the system of linear equations.

#### What is a system of equations?

AnswerA system of equation just means 'more than 1 equation.'. A * system of linear equations* is just more than 1 line, see the picture:

#### Ok, so what is the __solution__ of a system of equations?

Answer
The solution is where the equations 'meet' or intersect. The red point is the solution of the system.

#### How many solutions can systems of linear equations have?

AnswerThere can be zero solutions, 1 solution or infinite solutions--each case is explained in detail below. Note: Although systems of linear equations can have 3 or more equations,we are going to refer to the most common case--a stem with exactly 2 lines.

**Case I:**

*1 Solution*This is the most common situation and it involves lines that intersect exactly 1 time.

**Case 2:**

*No Solutions*This only happens when the lines are parallel. As you can see, parallel lines are not going to ever meet.

Example of a stem that has no solution:

**Line 1:**y = 5x +13**Line 2:**y = 5x + 12

**Case 3:**

*Infinite Solutions*This is the rarest case and only occurs when you have the __same line__

Consider, for instance, the two lines below (y = 2x+1 and 2y = 4x +2). These two equations are really the same line .

Example of a system that has infinite solutions:

**Line 1:**y = 2x + 1**Line 2:**2y = 4x + 2

##### Example 1

The **solution of the system of equations **on the left is (2,2) which marks the point where the two lines intersect.

#### How can we find solutions to systems of equations?

To find the solution to systems of linear equations, you can any of the methods below:

**Video**

on Solutions of Systems of Equations