Topics Linear Inequalities Systems of Linear Equations Inequalities

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Topics: • Linear Inequalities • Systems of Linear Equations • Inequalities

Topics: • Linear Inequalities • Systems of Linear Equations • Inequalities

Sec 2. 3 – Systems of Equations Steps for the Graphing Calculator: 1. Put

Sec 2. 3 – Systems of Equations Steps for the Graphing Calculator: 1. Put equations into y= screen 2. Hit Zoom Fit (#0) 3. Adjust window to see intersection 4. Hit 2 nd TRACE and choose #5 5. Hit ENTER 3 times 6. Interpret answer

Thus, the company will break even on this product if 12 thousand tons of

Thus, the company will break even on this product if 12 thousand tons of the product are sold, when both the cost and revenue equal $67, 020.

Solving Systems with Substitution

Solving Systems with Substitution

Practice with Substitution *look for the variable by itself A. 2 x – 3

Practice with Substitution *look for the variable by itself A. 2 x – 3 y = 6 x = -12 y B. 3 x = y x - 2 y = 26

Elimination/Combination is best used when both equations in the system are in standard form

Elimination/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. 4 x – 2 y = 7 * Are the equations in standard form? x + 2 y = 3

Forcing an Elimination A. 4 x + 9 y = 2 2 x –

Forcing an Elimination A. 4 x + 9 y = 2 2 x – 5 y = 6 B. -5 x + 8 y = 16 12 x + 24 y = 15

Investments An investor has $300, 000 to invest, part at 12% and the remainder

Investments 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?

Sec 2. 4 – Solutions of Linear Inequalities Inequality Signs There are 4 inequality

Sec 2. 4 – Solutions of Linear Inequalities Inequality Signs There are 4 inequality signs Fill in the blank: > Greater than 1. -2 ____ 4 ≥ Greater than or Equal to 2. 5 _____ 3 < Less than True or False: ≤ Less than or Equal to 3. -5 ≤ -11 4. 21 > 12

Graphing Inequalities on a Number Line Graph the following on a number line: X

Graphing Inequalities on a Number Line Graph the following on a number line: X > -4 X≤ 7

Solving Inequalities Special Rule: You MUST flip the inequality sign when you multiply or

Solving Inequalities 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

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 Sec. 2. 3 Pg. 134 -136 #3 -5 all #11 -17 odd (Must

Assignment Sec. 2. 3 Pg. 134 -136 #3 -5 all #11 -17 odd (Must show work to receive any credit) #25 -29 odd (Must show work to receive any credit) #42, 44, 52 Sec. 2. 4 Pg. 146 -149 #1 -7 odd (Must show work to receive any credit) # 13 - 15 odd (Must show work to receive any credit) #21 -25 odd (Must show work to receive any credit) #33 NOTE: • Quiz 1 due today August 27. • First Exam will be Tuesday September 2 Covers both Chapters 1 and 2.