1. Graphing Systems of Equations
Objective:
Use graphs to represent the solution

2. Solve by Graphing
1. Write the equations in slope-intercept form. 2. Use slope and y-intercept and graph lines on the same graph. 3. Determine the point of intersection and write as an ordered pair.

3. Parallel lines - no solution Same line –infinitely many solutions
Ordered Pair – 1 point

8. Example
x – y = 2 3y + 2x = 9

9. Example
x – y = 2
3y + 2x = 9
Step 1: Write each equation in slope-intercept form.
3y + 2x = 9
- 2x -2x
x – y = 2
- x - x
3y = -2x + 9
- y = - x +2 3 3 3
y = x - 2

10. Example x y
Step 2: Use the slope and y-intercept of each line to plot two points for each line on the same graph.
Step 3: Determine the point of intersection.
The point of intersection of the two lines is the point (3,1).
This system of equations has one solution, the point (3,1) .

11. You Try It

12. Problem 1 y The two equations in slope-intercept form are: x
Plot points for each line.
Draw in the lines.
These two equations represent the same line.
Therefore, this system of equations has infinitely many solutions .

13. You Try It

14. Problem 2 y The two equations in slope-intercept form are: x
Plot points for each line.
Draw in the lines.
This system of equations represents two parallel lines.
This system of equations has no solution because these two lines have no points in common.

15. You Try It

16. Problem 3 y The two equations in slope-intercept form are: x
Plot points for each line.
Draw in the lines.
This system of equations represents two intersecting lines.
The solution to this system of equations is a single point (3,0) .