Systems of Equations |
---|

Two or more equations put together are called Systems of Equations. |

Below, we have a system of equations:

2y = x + 1

3x = 4y - 1

The solution of a system of equations is called an ordered pair (x, y).

Below are examples of some of the linear and quadratic functions we've already learned about:

Figure 1. |
---|

Quadratic Systems |
---|

Quadratic systems are sets of quadratic equations that have variables with the same values. For example: The solution of a system of equations is called an ordered pair (x, y). There may be multiple (or no) solutions. |

Figure 2. |
---|

The above system has a solution at (0, -4).

Figure 3. |
---|

The above system has two solutions at roughly (0, -0.2) and (5, 2.8).

Figure 4. |
---|

The above system has no solutions.

Let's solve the system of equations below:

Figure 5. |
---|

To graph, first we must convert both equations to slope-intercept form:

Figure 6. |
---|

Now, we graph the equations:

Figure 7. |
---|

This system of equations has no solution.