1. 3/25 Bell Ringer Solve the system of equations: Remember to use your calculator Homework: Finish today’s Independent Practice.

2. News and Notes Today: BINDER BOOT CAMP Tomorrow: Binder Check Thursday: Concept Quiz Friday: 3 rd quarter grades go in

3. 3/28 Agenda I CAN identify number of solutions to a given system of equations. 1.Bell Ringer 2.New Material – 3 examples 3.Guided Practice – 3 more examples 4.Independent Practice – Try it on your own.

4. Example 1 Y = 3x + 5 -2x + y = 5 Given the above system of equations, identify number of solutions. Step 1: Get both in slope-int form (calculator ready form) Step 2: Graph both and sketch graph on paper. Step 3: Find intersections

5. Step 1: Get both in slope-int form (calculator ready form) Y = 3x + 5  OK! -2x + Y = 5  Needs fixed up +2x Y = 2x + 5  OK!

6. Step 2: Graph both and sketch graph on paper

7. Step 3: Find intersections How many solutions? ONE SOLUTION

8. Example 2 Y = 3x + 5 -3x + Y = 1

9. Step 1: Get both in slope-int form (calculator ready form) Y = 3x + 5  OK! -3x + Y = 1  Needs fixed up +3x Y = 3x + 1  OK!

10. Step 2: Graph both and sketch graph on paper

11. Step 3: Find intersections? When we have equations y = 3x + 5 and y = 3x + 1 where do the lines intersect? THEY DON’T! PARALLEL LINES = NO SOLUTIONS!

12. Example 3 Y = 3x + 5 -3x + y = 5 Given the above system of equations, identify number of solutions. Step 1: Get both in slope-int form (calculator ready form) Step 2: Graph both and sketch graph on paper. Step 3: Find intersections

13. Step 1: Get both in slope-int form (calculator ready form) Y = 3x + 5  OK! -3x + Y = 5  Needs fixed up +3x Y = 3x + 5  OK!

14. Step 2: Graph both and sketch graph on paper

15. Step 3: Find intersections How many solutions? INFINITE SOLUTIONS

16. Summarize – Guided Practice How many solutions are there to a system of equations that only has 1 intersection? - ONE How many solutions are there to a system of equations that appear to be parallel? - NO SOLUTIONS If a system of equations has no solutions, what will be true about the slope of the two equations? - SLOPES WILL BE THE SAME If a system of equations has no solutions, what will be true about the y-intercept? - Y-INT HAVE TO BE DIFFERENT If a system of equations has infinitely many solutions, what is true about the slope and y-intercept? - THEY ARE BOTH THE SAME  SAME EXACT SLOPE-INT EQUATION

17. Exit Ticket: Determine which system of equations has no solution. Show work