Warm Up # 6

HW Check – Word Problem Worksheet1) 10 adults, 11 children

2) 5 chicken dinners, 1 steak dinner

3) $8.50 per pizza, $2 breadsticks

4) $0.22 per mile, $36 per day

5) $0.30 per pound of flour, $0.40 per pound of sugar

6) 150 adults, 80 students, 48 children under 12

7) The three sides are 4cm, 7cm, 8cm

8) 3 nickels, 5 dimes, 17 quarters

9) No unique solution

Systems of Inequalities

§ 2.7 & 3.3

By the end of today, you should be able to…

Graph and interpret linear and absolute value inequalities.

Solve systems of linear inequalities.

Two-Variable Inequalities§ 2.7

Definitions & ProceduresLinear inequality: an inequality in two variables

whose graph is a region of the coordinate plane that is bounded by a line.

To graph:1. Graph the boundary line

2. Decide which side of the line contains solutions to the inequality and whether the boundary line is included.

Identify!1. Which of the graphs best

represents the inequality x ≥ 2?

2. Which of the graphs best suits the inequality y < 1?

3. Which graph best represents the inequality

x – y ≤ -3?

4. Which of the graphs best suits the inequality y ≤ 5x + 3?

Find which ordered pairs from the given set are part of the solution set for the inequality.

x + 2y < -7

{(0, 0), (8, -8), (-1, -3), (-5, 3)}

Graph the solution to the given inequality.

1. y < ½x – 3 2. y ≤ lxl

It takes a librarian 1 minute to renew an old library card and 3 minutes to make a new card. Together, she can spend no more than 30 minutes renewing and making cards.

a) Write an inequality to represent this situation, where x is the number of old cards she renews and y is the number of new cards she makes.

b) Can the librarian renew 12 old cards and create 7 new ones in 30 minutes or less?

Systems of Inequalities§ 3.3

Systems of InequalitiesTo graph a system of

inequalities, graph each inequality on the same Cartesian grid.

Key concept: Every point in the region of overlap is a solution of both inequalities and is therefore a solution of the system.

1. 2.

Tell whether (-3, 3) is a solution of each system.

ExamplesSolve each system of inequalities by graphing.

1. 2.