1. Lesson 7.5 Solve Special Types of Linear Systems
Essential Question: How can you identify the number of solutions of a linear system?

2. Before we start…
Graph 𝑦=− 1 2 𝑥+2 and 𝑦=− 1 2 𝑥−3 in the same coordinate plane.
What do you notice about these lines?

3. Classifying Systems CONSISTENT INCONSISTENT
-A system that has at least one solution
*INDEPENDENT
Exactly one solution
*DEPENDENT
Infinitely many solutions
INCONSISTENT
-A system that has no solution

5. How do you identify the number of solutions ?
The slope and y-intercept can tell you the number of solutions.
Number of Solutions
Slopes and y-intercepts
One solution
Different slopes
No solution
Same slope
Different y-intercepts
Infinitely many solutions
Same y-intercept

6. Graph the system. Tell how many solutions the system has.

7. Graph the system. Tell how many solutions the system has.

8. Graph the system. Tell how many solutions the system has.

9. Graph the system. Tell how many solutions the system has.

10. Graph the system. Tell how many solutions the system has.

11. Graph the system. Tell how many solutions the system has.

12. Solve the linear system algebraically.

13. Solve the linear system algebraically.

14. Solve the linear system algebraically.

15. Solve the linear system algebraically.

16. Solve the linear system algebraically.

17. Solve the linear system algebraically.

18. How can you identify the number of solutions of a linear system?

19. Ticket Out the Door
How many solutions does this system have?