Graphing Systems of Equations and Inequalities January 9

Graphing Systems of Equations and Inequalities January 9, 2013

Notes Setup Standards Toolbox • 9. 0 Students solve a system of two linear equations or linear inequalities and are able to interpret them graphically • 6. 0 Sketch the region defined by a linear inequality • • System of equations System of inequalities Consistent Independent Dependent Inconsistent Half-plane Boundary

Section 6 -7: GRAPHING INEQUALITIES IN TWO VARIABLES

Get Ready for the Lesson • Hannah budgets $30 a month for lunch. On most days, she brings her lunch. She can also buy her lunch at the cafeteria or at a fast food restaurant. She spends an average of $3 for lunch at the cafeteria and an average of $4 for lunch at the restaurant. How many times a month can Hannah buy her lunch and remain within her budget.

Solution There are many solutions for this inequality. Each solution represents a different combination of lunches bought in the cafeteria and the restaurant.

Graphing Linear Inequalities • The solution set for an inequality in two variables contains many ordered pairs when the domain and range are a set of numbers.

Graphing Linear Inequalities • The graphs of these ordered pairs fill a region on the coordinate plane called a halfplane. An equation defines the boundary or edge of each half-plane.

Graph the following: •

Real World Example • Neil wants to run a marathon at a pace of at least 6 miles per hour. Write an inequality for the miles y he will run in x hours and graph the solution set.

Answer •

More Practice • P. 337 #’s 1 – 7

Graphing Systems of Equations System of Equations: two or more equations together Consistent: if the graphs intersect (or coincide at one point); it has exactly one ordered pair to satisfy both equations Independent: it has exactly one solution Dependent: it has an infinite number of solutions Inconsistent: the graphs are parallel; there are no ordered pairs that satisfy both

Example #1

Answers to Example #1 1. 2. 3. 4. One No solution Infinitely many One

Example #2 Graph Each System of Equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If it has one solution, name it.

Answers to Example #2 a

Answer to #2 b INFINITELY MANY

Example #3

Example #3 Continued 1. Write the equation for each equation 2. Graph each equation: y = 3 x + 418 y = 8 x + 309 3. Look for the intersection (22, 485) Based on the information, both will be the same 22 years after 2004, or 2026

Your Turn

w= 2/3 length Answer 2 l + 2 w = 60 w = 2/3 l Border: P=60 length Now write each equation in terms of l and w w = 2/3 l w = l + 30

Answer continued (18, 12) There are 18 bricks along one edge and 12 bricks along the other.

Your Turn • The length of the rectangle is 1 meter less than twice its width. What are the dimensions of the rectangle?

Answer • •

Summary: • Pretend you are explaining how to graph inequalities to a friend. Explain all the steps needed to complete a problem. • When solving a system of equations by graphing, how do we find the answer?

Homework: • P. 256 #’s 17 -27 odd, 34 -36, 40 • P. 337 -338 #’s 9 -17 odd, 20 -22, 27 -30, 35, 36