1. Solving Systems of Equations By Graphing
A-REI.3; A-REI.5; A-REI.6; A-REI.7

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 f(x) = 4x – 1 2. g(x) = ½x h(x) = -x

4. Learning Intention/Success Criteria
LI: We are learning how to solve a system of equations by graphing SC: I know how to -determine is a system of equations has many, none, or no solutions -solve systems of two linear equations in two unknowns by graphing -read solutions to systems of equations off the graph of two functions -graph a linear equation

5. EQ: How Do I Solve a System of Equations by Graphing?
5/12/2019

6. A set of two or more equations that contain two or more variables, including nonlinear equations
System of Equations

7. The ordered pair(s) that satisfy all equations in the system at the same time
Solution to a system
Called the point of intersection
Three different types: no solution, many solutions, one solution

8. One Solution
The two lines cross each other in exactly one time on the graph
Infinite Solutions
The two lines are graphed on top of each other
No Solution
The two lines never cross each other

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

10. 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

11. Staple
Staple
Staple
One Solution x = a

12. Staple
Staple

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

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

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

16. Staple
Staple
Staple
One Solution x = a

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

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

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

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

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

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