Math3H - Unit 2 Day 2 SYSTEMS OF LINEAR INEQUALITIES Solving Linear Systems of Inequalities by Graphing

Math3H - Unit 2 Day 2 SYSTEMS OF LINEAR INEQUALITIES OBJECTIVES: 1) Apply systems of equations to real world situations 2) Graph a linear inequality 3) Graph the solution of a system of inequalities

Applications of System of Equations 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 Panther Creek High School and Enloe HS planned separate trips to New York City. The senior class at PCHS 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.  

Example 3: Matt and Ming are selling fruit for a school fundraiser 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.

Solving Systems of Linear Inequalities We show the solution to a system of linear inequalities by graphing them…Why is that? This process is easier if we put the inequalities into Slope-Intercept Form, y = mx + b. The < > sign will tell us how to shade the graph.

Solving Systems of Linear Inequalities Graph the line using the y-intercept & slope. If the inequality is < or >, make the lines dotted If the inequality is < or >, make the lines solid.

Solving Systems of Linear Inequalities The solution also includes points not on the line, so you need to shade the region of the graph: Shade above for y > or y  Shade below for y < or y ≤

Solving Systems of Linear Inequalities Example: a: 3x + 4y > - 4 b: x + 2y < 2 Put in Slope-Intercept Form:

Solving Systems of Linear Inequalities Example, continued: Graph each line, make dotted or solid and shade the correct area. a: dotted shade above b: dotted shade below

Solving Systems of Linear Inequalities a: 3x + 4y > - 4

Solving Systems of Linear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2

Solving Systems of Linear Inequalities a: 3x + 4y > - 4 b: x + 2y < 2 The area between the green arrows is the region of overlap and thus the solution.

Checking your Solution a: 3x + 4y > - 4 b: x + 2y < 2 Choose a test point in the solution region and check it in both equations – ex. (0, 0)

Checking your Solution a: 3x + 4y > - 4 b: x + 2y < 2 3*0 + 4*0 > -4 0 + 2*0 < 2 Both are TRUE!

You try it! Example 2: x + 2y > -12 -3x + y < 8 Put in Slope-Intercept Form Graph…solid or dotted? shade above or below? c) Solution area?

Unit 2 Quiz 1 Day 1 and 2 only You should be able to: Tell how many solutions Solve systems of equations and inequalities

U2 Day 2 HW In Weebly

TEACHER NOTES In Weebly