Topics: Linear Inequalities Systems of Linear Equations Inequalities.

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Presentation transcript:

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

Solving Systems with Substitution

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

Elimination/Combination 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 Inequalities Inequality 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 ____ _____ 5 True or False: 3.-5 ≤ > 12 Fill in the blank: 1.-2 ____ _____ 5 True or False: 3.-5 ≤ > 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! 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 Graphing Double Inequalities: “And” statements make a line segment “Or” statements go opposite of each other or overlap

Inequalities in Real-Life

Assignment