1. Solving Systems of Equations by Graphing

2. Table of Contents
46: Warm-Up
47: How Do I Solve a System of Equations by Graphing?

3. Warm Up
Graph the following equations on the same coordinate grid. Graph each equation in a different color.
1. f(x) = 4x – g(x) = ½x h(x) = -x 4. x = y = -3

4. Warm-Up
1. f(x) = 4x – g(x) = ½x h(x) = -x 4. x = y = -3

5. Learning Intention/Success Criteria
LI: We are learning how to solve a system of equations by graphing SC: I know how to -determine if a system of equations has many, none, or one solution(s) -solve systems of two linear equations in two unknowns by graphing -read solutions to system of equations off the graph of two functions -graph a linear equation

6. EQ: How Do I Solve a System of Equations by Graphing?
5/5/2019

7. System of Equations
A set of two or more equations that contain two or more variables, including nonlinear equations
Solution to a System
The ordered pair(s) that satisfy all equations in the system at the same time
Called the point of intersection
3 solution types: no solution, many solutions, one solution

8. One Solution
The two lines cross each other in exactly one spot on the graph
There will be an answer for x and y
Solution written: (x, y)

9. Infinite Solutions
Two lines are graphed on top of each other
Both sides of the equation will equal the same thing
No Solution
The two lines never cross each other
The two sides of the equations will not equal each other

10. Fold both papers with the white paper on the inside

11. Staple
Staple
Staple
1. Staple the whole packet three times near the fold 2. Cut only the top two layers, creating three spaces in total

12. Staple
Staple
Staple
One Solution x = a

13. Staple
Staple

14. Solve by graphing: {
y = -1/3x + 3 y = 2x - 4
Solution:
(3, 2)

15. { Guided Practice 1 Find the solution to the given system by graphing:
y = 2x - 5 y = -3x
Solution:
(2, -1)

16. Staple
Staple
Staple
No Solution a = b
One Solution x = a

17. Staple
Staple
Staple
One Solution x = a

18. Solve by graphing: {
y = -4/3x + 5 y = -4/3x
Solution:
No Solution

19. { Guided Practice 2 Find the solution to the given system by graphing:
y = 2x + 4 y = 6x
Solution:
No Solution

20. Staple
Staple
Staple
No Solution a = b
Many Solutions a = a
One Solution x = a

21. Staple
Staple
Staple
No Solution a = b
One Solution x = a

22. Solve by graphing: {
y = 3x - 1 y = 3x - 1
Solution:
Many Solutions

23. { Guided Practice 3 Find the solution to the given system by graphing:
y = -2x - 1 y = -4x –
Solution:
Many Solutions