1. 3-1 Graphing Systems of Equations
SWBAT:
1) Solve systems of linear equations by graphing.
2) Determine whether a system of linear equations is consistent and independent, consistent and dependent, or inconsistent.

2. What is a System of Equations?
A System of Equations is two or more equations with the same variables
The solution to a system of equations is the ordered pair that is a common solution of all the equations
One way we can solve a system of equations is by graphing the equations on the same coordinate plane

3. Lets Look at our Packet…
They intersect at (2,4), and both have it as a solution.

4. Look at another…
So they both have (-1,4) as a solution.

5. One more!
y = 4/3 x - 4
y = 2/3 x - 6
So they both have (-3,-8) as a solution.

6. Consistent and Independent
When two lines intersect, a System of Linear Equations has one solution (meaning only one point is a solution to both Equations).
When a system has one solution, the system is said to be consistent and independent.

7. Wait…What About?
These two lines are parallel! They have same exact slope
They will never intersect!

8. A system of equations might have no solution.
This would occur if the equations never intersect (they are parallel). They have no common coordinates.
When a system of equations has no solution, the system is said to be inconsistent.

9. What happens here? y = -5x - 2 These two lines the same equation!
They are the same exact line!

10. A system might have infinitely many solutions.
This would occur if the equations are the same exact line.
All the coordinates are the exact same.
When a system of equations has infinitely many solutions, the system is said to be consistent and dependent.

11. Summary…

12. Try Some

13. Try Some More…

14. Just a Few More