1. 3.7 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Are the ordered pairs a solution to the problem?

2. 3.7 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Are the ordered pairs a solution to the problem?

3. . 3.7 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Are the ordered pairs a solution to the problem? .

4. 3.7 - Graphing LinearInequalities
Graphing Inequalities in Two Variables
Graph the solution.

5. 3.7 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution.

6. 3.7 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution.

7. 3.7 - Graphing Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution.

9. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing
A system of linear equations allows the relationship between two or more linear equations to be compared and analyzed.

10. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing
Determine whether (3, 9) is a solution of the following system.
Both statements are true, therefore (3, 9) is a solution to the given system of linear equations.

11. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing
Determine whether (3, -2) is a solution of the following system.
Both statements are not true, therefore (3, -2) is not a solution to the given system of linear equations.

12. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing

13. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing

14. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing

15. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing
Special Systems of Linear Equations
Consistent system has at least one solution.
Inconsistent system has no solution.
Independent equations have different graphs.
Dependent equations have identical graphs.
Consistent system
Independent equations

16. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing
Special Systems of Linear Equations
Consistent system has at least one solution.
Inconsistent system has no solution.
Independent equations have different graphs.
Dependent equations have identical graphs.
Inconsistent system
Independent equations

17. Solving Systems of Linear Equations by Graphing
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Graphing
Special Systems of Linear Equations
Consistent system has at least one solution.
Inconsistent system has no solution.
Independent equations have different graphs.
Dependent equations have identical graphs.
Consistent system
Dependent equations

18. Solving Systems of Linear Equations by Substitution
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Substitution
Solution

19. Solving Systems of Linear Equations by Substitution
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Substitution
Solution

20. Solving Systems of Linear Equations by Elimination
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Elimination

21. Solving Systems of Linear Equations by Elimination
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Elimination
Solution

22. Solving Systems of Linear Equations by Elimination
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Elimination
Solution

23. Solving Systems of Linear Equations by Elimination
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Elimination
Solution

24. Solving Systems of Linear Equations by Elimination
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Elimination
Solution
(lines are the same)

25. Solving Systems of Linear Equations by Elimination
4.1 - Systems of Linear Equations (2 variables)
Solving Systems of Linear Equations by Elimination
No Solution
(lines are parallel)

26. 4.3 - Systems of Linear Equations and Problem Solving
The consumption of red meat and poultry are defined by the given equations, where x represents the number of years since 2003 and y represents the pounds per year consumed. In what year will the consumption be the same?
Substitution Method

27. 4.3 - Systems of Linear Equations and Problem Solving
The consumption of red meat and poultry are defined by the given equations, where x represents the number of years since 2003 and y represents the pounds per year consumed. In what year will the consumption be the same?
Substitution Method

28. 1st number is x, 2nd number is y
4.3 - Systems of Linear Equations and Problem Solving
A first number is seven greater than a second number. Twice the first number is four more than three times the second number. What are the numbers?
1st number is x, 2nd number is y
Substitution Method
Solution

29. 4.3 - Systems of Linear Equations and Problem Solving
Two trains leave Tulsa, one traveling north and the other south. After four hours, they are 376 miles apart. If one train is traveling ten miles per hour faster than the other, what is the speed of each train?
Train
Rate
Time
Distance
North
South x 4 4x y 4 4y
Substitution Method

30. 4.3 - Systems of Linear Equations and Problem Solving
One solution contains 20% acid and a second solution contains 50% acid. How many ounces of each solution should be mixed in order to have sixty ounces of a 30% solution?
Solution
Ounces
Decimal
Pure Acid
20%
50%
30% x
0.2
0.2x y
0.5
0.5y 60
0.3
(60)(0.3)

31. 4.3 - Systems of Linear Equations and Problem Solving
One solution contains 20% acid and a second solutions contains 50% acid. How many ounces of each solution should be mixed in order to have sixty ounces of a 30% solution?
Elimination Method

32. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the Union.

33. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution (Graph the intersection).

34. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the union.

35. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution. (Graph the intersection)

36. 4.5 – Systems of Linear Inequalities
Graphing Inequalities in Two Variables
Graph the solution. (Graph the intersection)