1. 4.1 Graphing Systems

2. Goals  SWBAT graph a system of linear equations and find the solution to the system.

3. Definitions  A of linear equations consists of or more lines in one coordinate plane.  The to a system of linear equation is the coordinates of the point of of the line(s). system one solution intersection

4. Three Possible Solutions 1. one solution (the lines intersect) These lines have the equations and What can you say about the slopes of the two equations that would help you to know that there is only one solution? What about the y-intercepts of the two equations?

5. Three Possible Solutions 2. no solution (the lines are parallel) These lines have the equations and What can you say about the slopes of the two equations that would help you to know that there is only one solution? What about the y-intercepts of the two equations?

6. Three Possible Solutions 2. Infinitely many solutions (the lines coincide) These lines have the equations and What can you say about the slopes of the two equations that would help you to know that there is only one solution? What about the y-intercepts of the two equations?

7. Determine the apparent solution set by graphing each system of equations. Show that each system satisfies one of the three possibilities (one, no solution, infinite solutions). 1.

8. Determine the apparent solution set by graphing each system of equations. Show that each system satisfies one of the three possibilities (one, no solution, infinite solutions). 2.

9. Determine the apparent solution set by graphing each system of equations. Show that each system satisfies one of the three possibilities (one, no solution, infinite solutions). 3.

10. Determine the apparent solution set by graphing each system of equations. Show that each system satisfies one of the three possibilities (one, no solution, infinite solutions). 4.

11. Systems of Three Equations  You can also find the point of solution for a system of three equations by graphing and finding the point of intersection.  If there is not a point that all three lines, meet, there is nosolution

12. Determine the apparent solution set by graphing each system of equations. Show that each system satisfies one of the three possibilities (one, no solution, infinite solutions). 5.