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Topics: β’ Linear Inequalities β’ Systems of Linear Equations Sec 2.3 β Systems of Equations 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) = 5585π₯ and its total cost by C(x) = 61740 + 440π₯, 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)? Steps for the Graphing Calculator: 1. Put equations into y= screen 2. Hit Zoom Fit (#0) 3. Adjust window to see intersection 4. Hit 2nd TRACE and choose #5 5. Hit ENTER 3 times 6. Interpret answer Solving Systems with Substitution Same Question βDifferent 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 π¦ = 5585π₯ and its total cost by π¦ = 61740 + 440π₯, 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 β 3y = 6 x = -12y B. 3x = y x - 2y = 26 Elimination/Combination 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. 4x β 2y = 7 * Are the equations in standard form? x + 2y = 3 Forcing an Elimination A. 4x + 9y = 2 2x β 5y = 6 B. -5x + 8y = 16 12x + 24y = 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 β Solutions of Linear Inequalities Inequality Signs There are 4 inequality signs Fill in the blank: > Greater than 1. -2 ____ 4 β₯ Greater than or Equal to 2. 4 _____ 5 < Less than True or False: β€ Less than or Equal to 3. -5 β€ -11 4. 21 > 12 Graphing Inequalities on a Number Line Graph the following on a number line: X > -4 Xβ€7 > OPEN Circles < β₯ CLOSED Circles β€ Solving Inequalities Solve & Graph the following inequalities: β’ 3π₯ + 7 β₯ 13 β’ 1 3 3 β 2π₯ < β4(π₯ + 1) β’ β 15 < 2x - 3 β€ 1) β’ 6π₯ β 2 β€ β4 or 3π₯ + 4 > 9 Special Rule: You MUST flip the inequality sign when you multiply or divide by a negative! Graphing Double Inequalities: βAndβ statements make a line segment βOrβ 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 studentβs 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