1. Examples

2. Example 1 Which of the points below are a solution to the graph of 2x + 3y = 6? a. (2.25, 0.5) b. (3.75, -0.5) c. (0, 2) d. (-6.75, 6.25)

3. Example 1 Which of the points below are a solution to the graph of 2x + 3y = 6? a. (2.25, 0.5) b. (3.75, -0.5) c. (0, 2) d. (-6.75, 6.25) Answer: A, B, and C all are solutions to this graph. D is not because when you plug -6.75 in for x you do not get a y value of 6.25.

4. Example 2 How many solutions are there to the graph of -x - 2y = 4.75? a. no solution b. one solution c. two solutions d. infinite number of solutions

5. Example 2 How many solutions are there to the graph of -x - 2y = 4.75? a. no solution b. one solution c. two solutions d. infinite number of solutions Answer: D. Because this is one linear function, and not a system, there is an infinite number of solutions.

6. Example 3 How many solutions are there to the system? Solve by graphing. -x - 2y = 4.75 2x + 3y = 6 a. no solution b. one solution c. two solutions d. infinite number of solutions

7. How many solutions are there to the system? Solve by graphing. -x - 2y = 4.75 2x + 3y = 6 a. no solution b. one solution c. two solutions d. infinite number of solutions Answer: B. The two graphs cross at one point so there is only one solution. Example 3

8. Using your calculator, estimate the solution to this system. You may have to Zoom to see the point of intersection. -x - 2y = 4.75 2x + 3y = 6 Example 4

9. Using your calculator, estimate the solution to this system. You may have to Zoom to see the point of intersection. -x - 2y = 4.75 2x + 3y = 6 Answer: The solution is approximately (-2.3,3.4) Your answer may be slightly different, but it should be very close to this. Example 4

10. Using your calculator, estimate the solution to this system. You may have to Zoom to see the point(s) of intersection. y = 4x + 1 y = 2 x Example 5

11. Using your calculator, estimate the solution to this system. You may have to Zoom to see the point(s) of intersection. y = 4x + 1 y = 2 x Answer: The solution is approximately (0, 1.01) AND (4.1, 17.4). There can always be more than one solution with non-linear systems, make sure you zoom enough to see the whole “picture”. Your answers may be slightly different, but they should be very close to these. Example 5

12. Example 6 Which of the points below are an approximate solution to the following system? y=3 x +1 y=2x-3 a. (-3.5, -4) b. (-1, 1.33) c. (-0.79, 1.42) d. (0, 3)

13. Example 6 Which of the points below are an approximate solution to the following system? y=3 x +1 y=2x-3 a. (-3.5, -4) b. (-1, 1.33) c. (-0.79, 1.42) d. (0, 3) Answer: C. (-0.79, 1.42) is the only point listed that is a solution to the system. *There is another solution to this system, but we are only looking at this one solution.

15. Find the solution to the system using a table. y=-1/2x+2 y=2x-3 Find the solution to the system using a table. y=-1/2x+2 y=2x-3 Start by creating a table for each equation: xyxy y=-1/2x + 2y = 2x - 3 Then you will want to start testing numbers using educated guesses. The numbers will tell you if you are getting closer or further from the solution.

16. Find the solution to the system using a table. y=-1/2x+2 y=2x-3 Find the solution to the system using a table. y=-1/2x+2 y=2x-3 xyxy y=-1/2x + 2y = 2x - 3 Then you will want to start testing numbers using educated guesses. The numbers will tell you if you are getting closer or further from the solution -2 0 4 1.5 11 45 -2 3 1 2 -7 2 1

17. Find the solution to the system using a table. y=-1/2x+2 y=2x-3 Find the solution to the system using a table. y=-1/2x+2 y=2x-3 xyxy y=-1/2x + 2y = 2x - 3 Is there and easier way? -2 0 4 1.5 11 45 -2 3 1 2 -7 2 1 You can enter these equations into your calculator as y1 and y2. Then, using the table function on your calculator you can scroll through the lists and find the solution(s) that works! There are a few things you need to remember though….

18. Keep in mind that… There can be MORE than one solution so you need to investigate a little deeper when finding solutions. Your calculator may not be set up to show the correct decimals, so the table function in the calculator will not always work, but it can get you started on the right path!

19. Find the solution to the system using a table. y=2 x +2 y=x+8 Find the solution to the system using a table. y=2 x +2 y=x+8 xy1 y2 y=2 x + 2y = x + 8 Plug the equations into your calculator for y1 and y2. Use the table function to find the solution. Make note of which equation is y1 and which is y2 Plug the equations into your calculator for y1 and y2. Use the table function to find the solution. Make note of which equation is y1 and which is y2

20. Find the solution to the system using a table. y=2 x +2 y=x+8 Find the solution to the system using a table. y=2 x +2 y=x+8 xy1 y2 1.54.82846.5 1.755.36366.25 266 2.256.75685.75 2.57.65695.5 2.758.72725.25 y=2 x + 2y = x + 8 Plug the equations into your calculator for y1 and y2. Use the table function to find the solution. Make note of which equation is y1 and which is y2 Plug the equations into your calculator for y1 and y2. Use the table function to find the solution. Make note of which equation is y1 and which is y2 This tells you the solution to the system is (2,6).