Download 5.6 Notes Alg1.notebook

5.6 Notes Alg1.notebook
January 10, 2013
5­6 Solving Systems of Linear Inequalities
Skills we've learned
1. Graph y < ­x + 4 and y ≤ x + 1
2. Write the inequality
to represent the graph:
3. You can spend at most $12.00 for drinks at a picnic. Iced tea costs $1.50 a gallon, and lemonade costs $2.00 per gallon. Write a system to represent this situation. Graph the solutions, describe reasonable solutions, and then give two possible combinations of drinks you could buy. Warm­up Answers
1. Graph y < ­x + 4 and y ≤ x + 1
2. Write the inequality
to represent the graph:
3. You can spend at most $12.00 for drinks at a picnic. Iced tea costs $1.50 a gallon, and lemonade costs $2.00 per gallon. Write a system to represent this situation. Graph the solutions, describe reasonable solutions, and then give two possible combinations of drinks you could buy. x ≥ 0
y ≥ 0
Only whole number solutions are reasonable. Possible answer: (2 gal tea, 3 gal lemonade) and (4 gal tea, 1 gal lemonade) 5.6 Notes Alg1.notebook
January 10, 2013
5­6 Solving Systems of Linear Inequalities
Graph and solve systems of linear inequalities in two variables
To help us make decisions based on numerous variables.
Identifying Solutions for Linear Inequalities 1. Tell whether the ordered pair is a solution of the system.
Substitute (­1,­3) for (x, y) in both inequalities to see if they are solutions to the inequalities.
y ≤ –3x + 1
y < 2x + 2
5.6 Notes Alg1.notebook
January 10, 2013
2. Tell whether the ordered pair is a solution of the system.
y < –2x – 1
y ≥ x + 3
Solving a System of Inequalities by Graphing
To show all the solutions of a system of linear inequalities, graph the solutions of each inequality. The solutions of the system are represented by the overlapping shaded regions. The first graph is what we did in the warm­up.
5.6 Notes Alg1.notebook
January 10, 2013
Solving a System of Inequalities by Graphing
3. Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions.
{
y ≤ 3
y > ­x + 5
Solutions: _____________ _____________ Not Solutions _____________ _____________ 4. Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions.
{ ­3x + 2y ≥ 2
y < 4x + 3
Solutions: _____________ _____________ Not Solutions _____________ _____________ 5.6 Notes Alg1.notebook
January 10, 2013
More if Needed. Graph the system of linear inequalities. Give two ordered pairs that are solutions and two that are not solutions.
Solutions: _____________ _____________ Not Solutions _____________ _____________ Graphing Systems with Parallel Boundaries
In Lesson 5­4, you saw that in systems of linear equations, if the lines are parallel, there are no solutions. With systems of linear inequalities, that is not always true.
This system has no solutions.
The solutions are all points between the parallel lines but not on the dashed lines.
The solutions are the same as the solutions of y ≥ 4x + 6.
5.6 Notes Alg1.notebook
January 10, 2013
5. Graph the system of linear inequalities. Describe the solutions.
B)
A)
This system has no solutions.
C)
The solutions are all points between the parallel lines including the solid lines.
The solutions are the same as the solutions of y > –2x + 3.
Application
In one week, Ed can mow at most 9 times and rake at most 7 times. He charges $20 for mowing and $10 for raking. He needs to make more than $125 in one week. Show and describe all the possible combinations of mowing and raking that Ed can do to meet his goal. List two possible combinations. Step 1 Write a system of inequalities.
Let x represent the number of mowing jobs and y represent the number of raking jobs.
x ≤ 9 y ≤ 7
20x + 10y > 125
Step 2 Graph the system. Shade
Step 3 Describe all possible combinations.
The graph should be in only the first quadrant because the number All possible combinations of jobs cannot be negative.
represented by ordered pairs of whole numbers in the solution region will meet Ed’s requirement of mowing, raking, and earning more than $125 in one week. Answers must be whole numbers because he cannot work a portion of a job.
Step 4 List the two possible combinations.
Two possible combinations are: 7 mowing and 4 raking jobs 8 mowing and 1 raking jobs
5.6 Notes Alg1.notebook
January 10, 2013
5.6 p.370 #3, 5, 7, 10, 15, 18 ­ 33 (x3), 37
Ch. 2 Study Guide p.150
#7, 8, 13, 15, 20, 30 ­ 32,
42, 49, 53, 63, 68, 74, 79
5.5
Review Ch. 1
5.6 Review Ch. 2
Review Review Ch. 5 Ch. 5 and Ch. 3 & 4
Test Ch. 5
Final Exam Review
5.4
No school
Review for Final
Day 1: Review for Chapter 2
Skills we've learned
2­1 Graphing and Writing Inequalities
2­2 Solving Inequalities by Adding or Subtracting
2­3 Solving Inequalities by Multiplying or Dividing
2­4 Solving Two­Step and Multi­Step Inequalities
2­5 Solving Inequalities with Variables on Both
2­6 Solving Compound Inequalities
2­7 Solving Absolute­Value Inequalities 5.6 Notes Alg1.notebook
January 10, 2013
2­1 Graphing and Writing Inequalities
1) Graph a. x > ­4
b.
2) Write an equation from a graph
a.
b.
2­2 Solving Inequalities by Addition/Subtraction
1) Solve and Graph
a. 7 + x < ­4 b. 6 > ­3 + x
2­3 Solving Inequalities by Multiply/Divide
a. ­4x > 9 b. 2­4 Solving Two­Step and Multi­Step Inequalities
a.
b. 2 < 3 + 7x
2­5 Solving Inequalities with Variables on Both
a.
b. 3x + 1 ­ 5x < 4 ­ 2x
5.6 Notes Alg1.notebook
January 10, 2013
2­6 Solving Compound Inequalities
a.
b. ­2x > 8 OR x + 4 > 10
2­7 Solving Absolute­Value Inequalities
a.
b.