1. WELCOME TO CHAPTER 7

2. Objectives: 1.Solve a system of equations by graphing. 2.Solve systems from the real world. Vocabulary: system of linear equations, solution to a system, point of intersection Solving Linear Systems by Graphing 7.1

3. We have solved equations like: We found many solutions to equations like: Now we will find one solution to two equations like: 3(x – 4) = 5x + 2(x – 3) = 5 – (x + 4) 2x + 4 = 12 x – 4 = 5 3x + 2y = 12y = 2x - 5 3x + 2y = 12y = 2x - 5 Solving Linear Systems by Graphing 7.1

4. Solving Linear systems by Graphing 7.1 Animal wolves cows bees birds crows fish lions turkeys monkeys alligators equations Group pack herd colony flock murder school pride rafters troop congregation system

5. Solving Linear systems by Graphing 7.1 Vocabulary: system of linear equations – a group of 2 or more equations that are linear – use a set mark { to group them. Vocabulary: system of linear equations To get 1 solution, you need the same number of equations as variables.

6. Example Solve the System by Graphing Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (3, 4)

7. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (-3, 1) Example Solve the System by Graphing

8. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (1, 3) Example Solve the System by Graphing

9. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 You Try Solve the System by Graphing

10. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 You Try Solve the System by Graphing

11. Solve the system by graphing. Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 You Try Solve the System by Graphing

12. Together Real Life Linear System You and your sister each have a savings account for college. You have $2000 and plan to deposit an additional $50 per month At the same time, your sister has a balance of $1600 and she plans to deposit $100 per month. Predict when you and your sister will have the same amount?

13. STANDS 0_23456789 Homework Assignment: Complete Graphing Worksheet! 7.1

14. Objectives: 1.Solve a system of equations by substitution. 2.Solve systems from the real world. Vocabulary: none Solving Linear Systems by Substitution 7.2

15. 1.Solve for one of the variables and star. 2.Substitute this into the other equation. 3.Solve for the only variable. 4.Substitute this value in the star equation. 5.Clearly state your answer. Order Pair! 6.Check the answer. How to Solve the System by Substitution

16. Which is the best variable to use for substitution. Solve a System by Substitution 1.Solve for one of the variables and star. 2.Substitute this into the other equation. 3.Solve for the only variable. 4.Substitute this value in the star equation. 5.Clearly state your answer. 6.Check the answer. Example Solve the System by Substitution

17. Solve the system by substitution. Solve a System by Substitution 1.Solve for one of the variables and star. 2.Substitute this into the other equation. 3.Solve for the only variable. 4.Substitute this value in the star equation. 5.Clearly state your answer. 6.Check the answer. Example Solve the System by Substitution

18. Solve the system by substitution. Solve a System by Substitution 1.Solve for one of the variables and star. 2.Substitute this into the other equation. 3.Solve for the only variable. 4.Substitute this value in the star equation. 5.Clearly state your answer. 6.Check the answer. Example Solve the System by Substitution

19. Solve the system by substitution. Solve a System by Substitution 1.Solve for one of the variables and star. 2.Substitute this into the other equation. 3.Solve for the only variable. 4.Substitute this value in the star equation. 5.Clearly state your answer. 6.Check the answer. You Try Solve the System by Substitution

20. Solve the system by substitution. Solve a System by Substitution 1.Solve for one of the variables and star. 2.Substitute this into the other equation. 3.Solve for the only variable. 4.Substitute this value in the star equation. 5.Clearly state your answer. 6.Check the answer. You Try Solve the System by Substitution

21. Solve the system by substitution. Solve a System by Substitution 1.Solve for one of the variables and star. 2.Substitute this into the other equation. 3.Solve for the only variable. 4.Substitute this value in the star equation. 5.Clearly state your answer. 6.Check the answer. Example Solve the System by Substitution

22. Solve the system by substitution. Solve a System by Substitution 1.Solve for one of the variables and star. 2.Substitute this into the other equation. 3.Solve for the only variable. 4.Substitute this value in the star equation. 5.Clearly state your answer. 6.Check the answer. You Try Solve the System by Substitution

23. In one day the Baseball Hall of Fame in Cooperstown admits 321 adults and children and collected $1590. The price of admission is $6 for an adult and $4 for a child. How many adults and how many children were admitted to the museum that day. 153 adults & 168 children Together Real Life Linear System

24. MEREPEAT Homework Assignment: Complete Substitution Worksheet! 7.2

25. Objectives: 1.Solve a system of equations by Linear Combinations. Vocabulary: none Solving Linear Systems by Linear Combinations 7.3

26. Linear Combinations (Elimination) Method Linear Combinations ( Elimination) method is used when it appears easy to eliminate one variable from the system through transformation. Remember that linear transformations do not change the solutions of a system.

27. Steps 1.Put equations in STANDARD FORM. 2.Multiply equations to create opposites. 3.Add equations together to create one new equation. 4.Solve for the first variable. 5.Substitute ^this^ variable into the top equation of the original system. 6.Solve for the second variable. 7.Check your answer!

28. Solve the system by Linear Combinations. Example Solve the System by LC

29. Solve the system by Linear Combinations. Example Solve the System by LC

30. Solve the system by Linear Combinations. Example Solve the System by LC

31. Solve the system by Linear Combinations. You Try Solve the System by LC

32. Solve the system by Linear Combinations. You Try Solve the System by LC

33. Solve the system by Linear Combinations. You Try Solve the System by LC

34. Homework Assignment: Complete Combinations Worksheet! 7.3

35. Objectives: 1.Graph systems of linear inequalities 2.Linear inequalities from real life Vocabulary: none Solving Systems of Linear Inequalities 7.6

36. Solve the System by Graphing Solve the system by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (3, 4) Solve a System by Graphing 1.Graph both equations. 2.Find the intersection. 3.Check the answer.

37. Solve the System by Graphing Solve the system by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 (3, 4) Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

38. Solve the system by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 Example 1 Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

39. Solve the system by graphing. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

40. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 Solve the system by graphing. Example 1 Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

41. 12 345 67 8 910 1 2 3 5 6 4 7 8 9 -6 -4-2 -8 -6 -2 -4 -8 Solve the system by graphing. Example 1 Graph a System of Inequalities 1.Graph both inequalities. 2.Find the intersection. 3.Check a solution.

42. My first is simply a vegetable, delicious, round and green. My third and fourth are sound asleep, as plainly can be seen. My fifth is fifty, clear enough for any riddle-setter. Two of my second stacked on their sides will give my final letter. Now that my second has my parts, fit them together well. You see me now before your eyes; it's plain for all to tell. Tonight’s Homework: Complete Graphing Inequalities Worksheet! Algebra 1

43. Answer Puzzle. My first is simply a vegetable, delicious, round and green. - Pea / P My third and fourth are sound asleep, as plainly can be seen. - ZZ My fifth is fifty, clear enough for any riddle-setter. - L (Roman Numeral) Two of my second on their sides will give my final letter. - E (Take 2 U's and stack them sideways.) Now that my second has my parts, fit them together well. - Now that YOU (u) have my parts... You see me now before your eyes; it's plain for all to tell.