Topics: Linear Inequalities Systems of Linear Equations Inequalities

Topics:

• Linear Inequalities

• Systems of Linear Equations

• Inequalities

MAT 150 Algebra

Class #7

Solving Systems by Graphing

A company is said to break even from the production and sale of a product if the total revenue (incoming $) equals the total cost. Suppose a company has its total revenue for a product given by R(x) and its total cost by C(x) , where x is the number of thousands of tons of the product produced and sold per year. When will the company break even or make profit P(x)?

Sec 2.3 – Systems of Equations

Steps for the Graphing Calculator:1. Put equations into y= screen2. Hit Zoom Fit (#0)3. Adjust window to see

intersection4. Hit 2nd TRACE and choose #55. Hit ENTER 3 times6. Interpret answer

Solving Systems with Substitution

Same Question –Different Method

A company is said to break even from the production and sale of a product if the total revenue (incoming $) equals the total cost. Suppose a company has its total revenue for a product given by and its total cost by , where x is the number of thousands of tons of the product produced and sold per year. When will the company break even?

Practice with Substitution

*look for the variable by itself

A. 2x – 3y = 6 B. 3x = y

x = -12y x - 2y = 26

Elimination/CombinationElimination/Combination is best used when both equations in the system are in standard form (Ax + By = C)

This method combines both equations by adding them together, but one of the variables must be eliminated as soon as the equations are combined.

4x – 2y = 7 * Are the equations in standard form?

x + 2y = 3

Forcing an Elimination

A. 4x + 9y = 2 B. -5x + 8y = 16

2x – 5y = 6 12x + 24y = 15

An investor has $300,000 to invest, part at 12% and the remainder in a less risky investment at 7%. If her investment goal is to have an annual income of $27,000, how much should she put in each investment?

Investments

Sec 2.4 – Solutions of Linear InequalitiesInequality Signs

There are 4 inequality signs

> Greater than

≥ Greater than or Equal to

< Less than

≤ Less than or Equal to

Fill in the blank:

1. -2 ____ 4

2. 4 _____ 5

True or False:

3. -5 ≤ -11

4. 21 > 12

Graphing Inequalities on a Number Line

Graph the following on a number line:

X > -4

X ≤ 7

OPEN Circles

CLOSED Circles

Solving Inequalities

Solve & Graph the following inequalities:

• – 15 2x - 3

Special Rule:You MUST flip the inequality sign when you multiply or divide by a negative!

Graphing Double Inequalities:“And” statements make a line segment

“Or” statements go opposite of each other or overlap

Inequalities in Real-Life

Course Average

To pass a course with a B average, a student must have an average of 80% or greater. A student’s grades on three tests are 75%, 83%, 72% and 86%. What grade must the student earn on the final test so that his course average is a B or better.

What would change if the student only wanted a B average?

Assignment