# 3 Situations for Linear Systems.

### Once, Always or Never!

## A simple system consists of two linear equations

When two lines are graphed on one coordinate plane three situations are possible

## The horse is faster, even if you have a head start! The point of intersection is where both lines are equal. This is called the solution to the system. In real life terms, this is where the horse catches you! | ## You and your friend run at the same rate! Each line could represent a different person. In this case the runners run at the same rate. These runners will never meet. The lines are parallel because they have they have the same rate (slope.) There will never be a solution to this system. | ## Same line graphed twice! In some cases the equations of lines can look different. Once you graph them they turn out to be the same line. In this case all coordinate points are in common. Therefore, there are infinite solutions to this this system. An example would be you and your friend racing. You start at the same place, your run at the same rate, and you are tied the entire way. |

## The horse is faster, even if you have a head start!

The point of intersection is where both lines are equal. This is called the solution to the system. In real life terms, this is where the horse catches you!

## You and your friend run at the same rate!

Each line could represent a different person. In this case the runners run at the same rate. These runners will never meet. The lines are parallel because they have they have the same rate (slope.) There will never be a solution to this system.

## Same line graphed twice!

In some cases the equations of lines can look different. Once you graph them they turn out to be the same line. In this case all coordinate points are in common. Therefore, there are infinite solutions to this this system. An example would be you and your friend racing. You start at the same place, your run at the same rate, and you are tied the entire way.