1. Systems of Linear Equations
7.6– PROPERTIES OF 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: Coincident lines:
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. EXAMPLE
Create a linear system with no solutions, one solution, and infinite solutions, given the equation -6x + y = 3.
Solutions: