#### 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:

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How to Solve Systems

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.

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.

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

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

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

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

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

on Solutions of Systems of Equations