#### What is a system of equations?

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

How to Solve Systems

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

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

There 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 at exactly one point.

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 III: *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

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

on Solutions of Systems of Equations