Solving Systems of Equations Using Graphs

1. Wednesday April 21st Bell Ringer: Write a system for the following problem. The sum of two numbers is 186. The difference between the same numbers is 32. Create a table to solve the system of equations and then check the solution.

2. The sum of two numbers is 186. The difference between the same numbers is 32. Create a table to solve the system of equations and then check the solution.

3. Today Objective: I CAN solve systems of equations using graphs

4. How can we solve this system of equations • Let’s use graphs • Remember, the solution to a system of equations is a point where both equations are _______________ • Using a graph, the solution to a system of equations is where is the point where the lines ___________________

5. How can we solve this system of equations • Let’s use graphs • Remember, the solution to a system of equations is a point where both equations are TRUE • Using a graph, the solution to a system of equations is where is the point where the lines ___________________

6. How can we solve this system of equations • Let’s use graphs • Remember, the solution to a system of equations is a point where both equations are TRUE • Using a graph, the solution to a system of equations is where is the point where the lines INTERSECT

7. Example #1 Let’s Use our graphing calculator to help solve this one

8. So how to use the calculator • Step 1: Hit y=. Enter the first equation into Y1 and the next into Y2. Use the picture below for reference.

9. Using Our Calculator • Step 2: Press ZOOM(the middle button on top), then Option 6: ZStandard – this will set up the window to have standard axes.

10. Using our calculators • Step 3: Press GRAPH (the button at the top right) to bring up the graph. See the picture below (our will look a bit different)

11. Using our calculators Step 4: Press 2ND, then the TRACE button (on the top row) to bring up the CALC menu (Display 7)

12. Using Our Calculators Step 5: Select option 5: intersect, then hit the ENTER button three times. Your screen should look like the picture below, with the point of intersection listed at the very bottom of the screen

13. So what did we get? So our solution is point (1,2) now we need to check our answer:

14. Let’s try a few more examples Example #2 Example #3 Example #4

15. Example #1 Our solution is (0.4, 1.2)

16. What did you notice about examples #2 and #3? So… 1. When the two lines are parallel there is … NO SOLUTION These lines have the same SLOPE but a different Y-INTERCEPT 2. When the lines are the same there is… INFINITE SOLUTIONS

17. Rest of Class Try finishing the back of the worksheet using your calculators We will go over the bonus problem at the end

18. Today’s Bonus Problem There are two special offers on candy. 79th street candy is offering a $2 initial fee and $0.50 for every pound frooties you buy. Pulaski candy is offering a deal with a $5 initial fee but charge only $0.10 for every pound of frooties. How many pounds of frooties do you have to buy for these two deals cost the same and how much will it cost?

19. Let’s write the system first There are two special offers on candy. 79th street candy is offering a $2 initial fee and $0.50 for every pound frooties you buy. Pulaski candy is offering a deal with a $5 initial fee but charge only $0.10 for every pound of frooties. How many pounds of frooties do you have to buy for these two deals cost the same and how much will it cost? • C= Total Cost

20. Let’s write the system first There are two special offers on candy. 79th street candy is offering a $2 initial fee and $0.50 for every pound frooties you buy. Pulaski candy is offering a deal with a $5 initial fee but charge only $0.10 for every pound of frooties. How many pounds of frooties do you have to buy for these two deals cost the same and how much will it cost?

21. How can we do this? Let’s use our calculators