1. Missy McCarthyOkemos High School S OLVING S YSTEMS USING GRAPHING

2. L EARNING T ARGETS What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary

3. W HAT IS A L INEAR S YSTEM ? What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary Two or more linear equations together form a system of linear equations.

4. S OLUTIONS TO A L INEAR S YSTEM What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary Any ordered pair (values for the variables) that makes ALL of the equations true is a SOLUTION of the system.

5. E XAMPLE : S OLVING BY GRAPHING What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary One way to find the solutions of a linear system is by graphing the equations in the system to find the point that they have in common. Find the solution to the system of equations by graphing. y = 2x – 3 y = x - 1

6. E XAMPLE : S OLVING BY GRAPHING What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary Find the solution to the system of equations by graphing. 3x + 4y = 12 2x + 4y = 8

7. E XAMPLE : A PPLICATION What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary I’m planning to take a Zumba class at Court One. I called to find out the costs and was told that it is $4 per class for non-members while members pay a $10 fee and an additional $2 per class. Write a system of equations to model the cost for non-members and members and solve by graphing. Interpret your solution.

8. S YSTEMS WITH N O S OLUTION What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary

9. S YSTEMS WITH M ANY S OLUTIONS What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary

10. S UMMARY What you will learn What is a linear system? Solutions to a linear system Example: Solving by graphing Example: Application Systems with no solution Systems with infinitely many solutions Summary Lines that intersect at one point have only one solution. These lines have different slopes. Lines that are parallel have no solution. These lines have the same slope and a different y- intercept. Lines that coincide/one lies right on top of the other have infinitely many solutions. These lines have the same slope and the same y-intercept.