1. LESSON 5 – PROPERTIES OF LINEAR SYSTEMS SYSTEMS OF LINEAR EQUATIONS

2. TODAYS OBJECTIVES Students will be able to solve problems that involve systems of linear equations in two variables graphically and algebraically, including: Explain, using examples, why a system of equations may have no solution, one solution, or an infinite number of solutions Explain a strategy to solve a system of linear equations Solve a problem that involves a system of linear equations

3. VOCABULARY Infinite: endless amount or number, unlimited Coincident lines: two lines that have the same graph (same slope and y-intercept)

4. PROPERTIES OF LINEAR SYSTEMS There are three possible solution sets in a system of linear equations: 1) One solution – Lines intersect once, different slopes 2) No solution – Parallel lines, same slope, different y-intercepts 3) Infinite solutions – same lines, same slopes, same y-intercepts

5. PROPERTIES OF LINEAR SYSTEMS

6. PROPERTIES OF LINEAR SYSTEMS

7. PROPERTIES OF LINEAR SYSTEMS

8. EXAMPLE One solution Infinite Solutions No Solutions

9. CREATING A LINEAR SYSTEM WITH 0, 1, OR INFINITE SOLUTIONS

10. CREATING A LINEAR SYSTEM WITH 0,1, OR INFINITE SOLUTIONS

11. CREATING A LINEAR SYSTEM WITH 0,1, OR INFINITE SOLUTIONS

12. YOUR TURN Create a linear system with no solutions, one solution, and infinite solutions, given the equation -6x + y = 3. Solutions:

13. HOMEWORK pg. 448-449, #6, 8, 12-17, 19-20, 23 Next class we will have an assignment to be handed in for marks. The class after that, we will have a Chapter 7 test.

14. ABCD QUIZ!