1. Warm-Up 1) Sketch a graph of two lines that will never intersect.
2) Sketch a graph of two lines that intersect at one point.
3) Sketch a graph of two lines that intersect at every point (an infinite number of points).

2. B10 Solving Systems of Equations by Graphing
Objectives:
To find the solution of a system of equations by graphing

3. Activity Part 1 - Graph the equation 2x + 3y = 12
How many points of intersection are there? 1

4. Activity Part 1 - Graph the equation x = 2y + 1
How many points of intersection are there?

5. Activity Part 1 - Graph the equation 2x = 4 - y
How many points of intersection are there?
an infinite number

6. Example 1 Solve the following system by graphing. x + y = 2 x = y x y2 -8 -6 -4 -2 2 4 6 8 1 1 5 -3
(1,1)
x = y x y 1 1 5 5

7. Practice Solve by graphing. x + 4y = -6 2x – 3y = -1 y + 2x = 5

8. Warm-Up 4 minutes Solve by graphing. 1) y – 2x = 7 y = 2x + 8

9. Example 1 Determine whether (3,5) is a solution of the system.
y = 4x - 7
x + y = 8
5 =
4( ) 3
- 7 3
+ 5
= 8
5 =
8 = 8
5 = 5
(3,5) is a solution of the system

10. Example 2 Determine whether (-2,1) is a solution of the system.
2x – y = -5
3x + 2y = 3
2( ) -2
- 1
= -5
3( ) -2
+ 2( ) 1
= 3
-4 – 1 = -5
= 3
-5 = -5
(-2,1) is not a solution of the system

11. Practice
Determine whether the given ordered pair is a solution of the system.
(2,-3); x = 2y + 8
2x + y = 1
(-3,4); 2x = -y – 2
y = -4

12. Practice Solve these systems by graphing. x + 4y = -6 2x – 3y = -1