Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Algebra IIA Algebra/Geometry Review: Systems of Equations and Inequalities Foundational Material o Ability to solve one step and multiple step equations and inequalities Goal o Find solutions that satisfy systems of equations o Ability to graph linear equations on a coordinate plane o Find solutions that satisfy systems of inequalities Why? o Build a foundation for higher level mathematics o Solve equations in Economics and Chemistry o Determine which purchases are better deals Key Vocabulary o Consistent system o Dependent system o Inconsistent system o Linear inequality o System of equations o Graph one or more inequalities on a coordinate plane o System of inequalities o Solution to a system Lesson 3: Graphing Systems of Inequalities Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables. (CC.9-12.REI.6) Explain why the x-coordinates of the points where the graphs of the equations y=f(x) and y=g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology to graph the functions, make tables of values,… (CC.9-12.REI.11) Create equations in two or more variable to represent relationships between quantities; graph equations on coordinate axes with labels and scales.* (CC.9-12.CED.2) Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. (CC.9-12.CED.3) Example #1: Graph y > 2x – 5 When do we use a dotted line? When do we use a solid line? When do we shade above the line? When do we shade below the line? Solution will be the set of ordered pairs that satisfy all the inequalities! Example #2 Example #3 Graph the system: Plot the graph of the system of inequalities. y > 2x – 5 1 y x3 3 3 x 2 y 12 -2x+5y > -10 x y 1 Is it possible for there to be no solution? If so, describe what the graphs would look like. Example #4 Plot the graph of the system of inequalities. 2 x6 y -1 x – 2y > -6 1 y 5 ( x 4) 2 Solve the system by graphing. 1) 2x – y = 10 x + 3y = -9 Solve the system by substitution. 2) 4x + y = -10 -3x + 5y = 19 Solve the system by elimination. 3) 2x – 4y = 5 3x – 6y = 8 Solve the problems that follow. 1. The difference between two numbers is 16. Three times the larger number is 9 times the smaller. What are the numbers? 2. Soybean meal is 16% protein and corn meal is 9% protein. How many pounds of each should be mixed together to get a 350 lb mixture that is 12% protein? 3. One canned juice drink is 15% orange juice and another is 5% orange juice. How many liters of each should be mixed together to get a 10 L solution that is 10% orange juice? 4. One day a store sold 30 sweatshirts. White ones cost $9.95 and yellow ones cost $10.50. In all, $310.60 worth of sweatshirts were sold. How many of each color were sold?