1. WARM-UP Complete the below problems. A) Find a solution to the linear equation: B) Sketch a graph of:

2. 3.1: SOLVING SYSTEMS USING TABLES AND GRAPHS Ms. Miller

3. TODAY’S OBJECTIVE To solve a linear system using a graph or table XY1Y2

4. LINEAR SYSTEMS Systems of equations: A set of 2 or more equations Linear system: Consists of linear equations Solution: A set of values for all variables that makes all the equations in the system true. Also known as the intersection point of the lines.

5. METHOD: SOLVE BY GRAPHING The lines have one intersection point. Therefore, the solution is (2,-1).

6. METHOD: SOLVE BY CREATING A TABLE We look for where the y-values are equal and use those values to create the ordered pair for our solution: (2,-1). This system is classified as independent. xY1Y2 -2 0 1 2 -3 11 -2.5 8 -2 5 -1.5 2

7. USING THE CALCULATOR Try these problems with your graphing calculator: 1. 2. 3. (-2,-3) (-1,-4) (-1,-2)

8. CLASSYIFYING SYSTEMS: INCONSISTENT When a system contains parallel lines, there is no solution.

9. CLASSYIFYING SYSTEMS: DEPENDENT When a system contains coinciding lines, there are infinitely many solutions.

10. WRAP-UP SystemsConsistent Independent –Dependent – Inconsistent No Solution – One Solution Infinitely Many Solutions Parallel Lines

11. APPLYING THE LESSON Coach Lee offers tennis lessons at $25 per hour. The Hunterdon Tennis Club charges $20 per hour and a registration fee of $10. A) Write a system of equations that represents the cost of tennis lessons in terms of hours. B) When are the costs the same? C) If you plan on practicing 10 hours a week, which option is better?

12. APPLYING THE LESSON 0 0 10 xY1Y2 1 25 30 2 50 50 3 75 70 A) B) 2 hours of instruction C) Hunterdon Tennis Club

13. TONIGHT’S HOMEWORK PAGES 138-139 7 – 9 & 12 (Create a table), 17-27 odd, 29 – 32 Bring charged Chromebooks tomorrow!