Topics Linear Inequalities Systems of Linear Equations Inequalities
- Slides: 13
Topics: • Linear Inequalities • Systems of Linear Equations • Inequalities
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 the product are sold, when both the cost and revenue equal $67, 020.
Solving Systems with Substitution
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 (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 – 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 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 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 > -4 X≤ 7
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 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 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.
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