1. SWBAT: SOLVE SYSTEMS OF LINEAR EQUATIONS BY GRAPHING GRAPH PAPER IS PREFERRED FOR THESE NOTES Solving Systems by Graphing

2. Why learn this? To solve problems by comparing costs for services like television. Write your reason for learning this at the top of your notes. When you are finished, put your pencils down.

3. Review: Graphing in Slope-intercept Form Slope intercept: y = mx + b  X, Y are coordinates of the line  B is the y-intercept (0, b)  M is the slope Slope describes how a line looks: Graphing slope-intercept: 3x + 2 = y  Find the y-intercept: (0, 2)  Move by the slope: up 3, over 1.

4. New Vocabulary Solution of a linear equation: all the pairs of x,y values that land on a line. Example: (0, 2) is a solution of the equation. (4,0) is a solution of the equation (-4, 4) is a solution

5. New Vocabulary System of linear equations: two or more linear equations together Aka, 2 graphs of a line on the same grid.

6. New Vocabulary Solution of the system: any ordered pair that is shared between two equations. Example: the point (1,3) is a solution of the system.

7. Solve the system of linear equations by graphing Step 1: graph line 1 Step 2: graph line 2 Find the point of intersection (you will need to have drawn a good graph!) Check the point by filling it back into both equations. Example: Y = 2x – 3 Y = x – 1 Check, is (2, 1) a solution to both? ✔ 1 = 2(2) – 3? Yes, solution checks for eqn. 1 ✔ 1 = (2) – 1? Yes, solution checks for eqn. 2 ✔ Checks for both. It is the solution

8. You try: Solve by graphing. Check your solution. Solve the system: y = x + 5 Y = -4x

9. You try: Solve by graphing. ANSWER Solve the system: y = x + 5 Y = -4x ✔ 4 = (-1) + 5 Yes. ✔ 4 = -4(-1) Yes. ✔ Yes, this point is a solution for both lines.

10. Solve by Graphing. Verify your answer. 1) y = -2/3x + 1 y = 3/2x – 1 2) Y = 4x + 5 Y = 2x – 1 3) Y = 2.5x – 3 Y = x 4) 7x – 3 = y 3x + 1 = y 5) 5x – 2 = y 2x + 1 = y 6) 4x = y 6x – 3 = y

11. Solve by Graphing. Verify your answer. 1) y = -2/3x + 1 y = 3/2x – 1 (12/13, 5/13) 2) Y = 4x + 5 Y = 2x – 1 ( -3, -7) 3) Y = 2.5x – 3 Y = x (2, 2) 4) 7x – 3 = y 3x + 1 = y (1, 4) 5) 5x – 2 = y 2x + 1 = y (1, 3) 6) 4x = y 6x – 3 = y (3/2, 6)

12. Think logically: Are there any lines that do not intersect? Parallel lines What does solution mean again? Where 2 lines intersect Is there going to be a solution for lines that do not intersect? No. When lines are parallel, there is no solution.

13. Think logically: Is there more than one way to represent the equation of the same line? Yes, slope-intercept form and Ax + By = C form. How many times does the same line intersect with itself? Infinitely many. How many solutions will there be for the equation of the same line? Infinitely many

14. Infinitely many solutions = same line No Solution = parallel Review (past 2 slides)

15. Sort your cards Sort your cards into groups based on whether they have 1 solution, no solution, or infinitely many solutions

16. Practice Complete Pg. 272 #1 – 45 odds only It will be collected at the end of the hour for a grade If you finish early, complete the exit ticket and pick up the homework.