1. Warm-up Determine if (2, 1) is a solution to the following
systems: Answer yes or no!

2. 3. Graph to find the solution.
y = 3x – 12
y = -2x + 3
Solution: (3, -3)

3. Homework ?s

4. Skllls Check

5. Foundations of Algebra
Today’s Topics:
1. What other solutions are possible when graphing systems?
2. Review of Solving For a Variable

6. Solve Systems of Equations by Graphing

7. Steps Make sure each equation is in slope-intercept form: y = mx + b.
Graph each equation on the same graph.
Three Types of Solutions:
Intersect at one point.
Parallel lines that do not intersect.
The exact same line that intersects all the time.

8. So basically….
If the lines have the same y-intercept b, and the same slope m, then the system has infinitely many solutions.
If the lines have the same slope m, but different y-intercepts b, the system has no solution
If the lines have different slopes m, the system has a solution at the one point of intersection.

9. 1:
Solution: (-1, 3)

10. 2:
No Solution

11. 3:

12. 4: You Try!

13. Solve One Variable Equations

14. Steps Remember to distribute first. Combine any like terms.
Isolate the variable.

15. 1:
Solution:
x = 6

16. 2:
Solution:
x = -4

17. 3:
Solution:

18. 4:
Solution:

19. 5:
Solution:

20. 6:
Solution:

21. Homework