Warm Up

• Solve the following system of equations using any method:

SYSTEMSOF

EQUATIONWORD PROBLEMS

Word Problems

• When working with system-of-equations word problems, determine the two equations that you can write.

• Then solve using any method

Example 1

• A test has twenty questions worth 100 points. The test consists of True/False questions worth 3 points each and multiple choice questions worth 11 points each. How many multiple choice questions are on the test?

Example 2• The senior classes at Knightdale High School

and Enloe HS planned separate trips to New York City. The senior class at KHS rented and filled 1 van and 6 buses with 372 students. EHS rented and filled 4 vans and 12 buses with 780 students. Each van and each bus carried the same number of students. How many students can a van carry? How many students can a bus carry?

Example 3

• Matt and Ming are selling fruit for a school fundraiser. Customers can buy small boxes of oranges and large boxes of oranges. Matt sold 3 small boxes of oranges and 14 large boxes of oranges for a total of $203. Ming sold 11 small boxes of oranges and 11 large boxes of oranges for a total of $220. Find the cost each of one small box of oranges and one large box of oranges.

GRAPHING LINEAR

INEQUALITIES

Step 1) Put the inequalities into slope-intercept form.

y = mx + bslope

y-intercept

We show the solution to a linear inequality with a graph.

Step 2) Graph the line

a) If the inequality is < or >, make the lines dotted.

b) If the inequality is < or >, make the lines solid.

Step 3) Shade the correct region of the graph:

a) Above the line for y > or y .

b) Below the line for y < or y ≤.

**This is because more then 1 ordered pair can be a solution!

Examples:

1) y > -5x + 4

Examples:

2) x < 4 3) y ≥ -3

Examples:

4) 2x – 3y ≤ 6

Careful when you divide by a negative!

Examples:

5) 3x + 2y < -2

SYSTEMS OF INEQUALITIES

We show the solution to a system of linear inequalities with a graph!

Steps to Graphing a System of Inequalities:1) Put the inequalities into slope-

intercept form.2) Decide if the lines should be dotted or

solid.3) Shade above for y > or y , shade

below for y < or y ≤.4) Shade the overlapping section darker

to show where the solutions to both inequalities lie.

Example #1: a: 3x + 4y > - 4

b: x + 2y < 2

Put in Slope-Intercept Form:

3: 1

4 a y x

1: 1

2 b y x

Graph each line, make dotted or solid and shade the correct area.

dottedshade

above

dottedshade below

#2 Graph the system of

linear inequalities.

x ³ –1

y > x – 2

#3x > -2y < 6-2x + y > -5

Class Work

• Graph the System of Inequalities on the handout

Homework

• HW 2.4