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ACC CCGPS Coordinate Alg./Analytic Geo. Unit 2 Systems Volume 1 Issue 2 References Dear Parents: Holt Mathematics Course 3 Text Connection: Chapter 11: Lesson 6 Chapter 12: Lesson 7 Extension Below you will find a list of concepts that your child will use and understand while completing Unit 2 Systems. Also included are references, vocabulary and examples that will help you assist your child at home. Concepts Students will Use and Understand Given a problem in context, write an appropriate system of linear equations or inequalities. Solve systems of equations graphically and algebraically, using technology as appropriate. Graph the solution set of a system of linear inequalities in two variables. Interpret solutions in problem contexts. Holt Mathematics Course 3 Text Online: Vocabulary http://go.hrw.com/reso urces/go_mt/hm3/so/c 3ch11bso.pdf Intersecting Lines: lines that have one point in common or all points in Coefficients: a numerical factor in a term of an algebraic expression. common. Linear Combination Method: a technique for solving a system of http://my.hrw.com/ma th06_07/nsmedia/hom ework_help/msm3/ms m3_ch11_06_homewor khelp.html equations that involves combining two equations in order to eliminate one of the variables and solving for the remaining variable. Adding, subtracting, or multiplying a system of equations to help solve the system. Substitution Method: a technique for solving a system of equations that involves replacing one variable with an equivalent expression and solving for the remaining variable. System of Linear Equations: two or more equations that together define a relationship between variables usually in a problem situation. A system of equations can have no solution, one solution, or many solutions. System of Inequalities: two or more inequalities that together define a relationship between variables usually in a problem situation. A system of inequalities can have no solution or multiple solutions Try http://intermath.coe.uga.edu/ for additional help. www.ceismc.gatech.edu/csi ACC CCGPS Coordinate Alg./Analytic Geo. Unit 2 Systems Symbols < Less than Less than or equal to > Greater than Example 1 Solve the system of equations using any method you choose. 2x + y= 7 x – 3y= 0 Greater than or equal to Example 2 Solve the system of inequalities by graphing: 4 y x4 7 y ≤ 2x+4 Example 3 A soccer team is scheduled to play 14 games during a season. Their coach estimates that it needs at least 20 points to make the playoffs. A win is worth 2 points and a tie is worth 1 point. Write a system of inequalities and determine how many ways there are for the team to make the playoffs. Key Links: Example 1 http://www.purplemat h.com/modules/systlin 1.htm (3,1) Example 2 http://www.regents prep.org/Regents/ math/ALGEBRA/AE3 /indexAE3.htm http://www.regents prep.org/Regents/ math/ALGEBRA/AE8 5/indexAE85.htm http://www.regents prep.org/Regents/ math/ALGEBRA/AE9 /indexAE9.htm Example 3 The two inequalities are: 2w y 20 and w y 14 . The solution region contains 25 combinations for the team to make the playoffs. ACC CCGPS Coordinate Alg./Analytic Geo. Unit 2 Equal or Not Volume 1 Issue 3 References Mathematics Course 3 Text Connection: Chapter 1: Lessons: 23, 7-8 Chapter 2: Lessons: 78 Chapter 11: Lessons: 1-5 Holt Mathematics Course 3 Text Online: http://go.hrw.com/reso urces/go_mt/hm3/so/c 3ch11aso.pdf http://go.hrw.com/reso urces/go_mt/hm3/so/c 3ch11bso.pdf http://go.hrw.com/hrw. nd/gohrw_rls1/pKeywo rdResults?keyword=mt 7+hwhelp11 http://go.hrw.com/mat h/extra/course3/3_10_ Music/3_10_Music_07. htm Dear Parents Below you will find a list of concepts that your child will use and understand while completing Unit 2 Equal or Not. Also included are references, vocabulary and examples that will help you assist your child at home. Concepts Students will Use and Understand Use algebraic expressions, equations, or inequalities in 1 variable to represent a given situation. Simplify & evaluate algebraic expressions, including those with exponents. Solve and interpret algebraic equations and inequalities in 1 variable, including those with absolute values. Graph the solution of an equation or an inequality on a number line. Vocabulary Absolute Value: The distance a number is from zero on the number line. Examples: |-4| = 4 and |3| = 3 Addition Property of Equality: For real numbers a, b, and c, if a = b, then a + c = b + c. In other words, adding the same number to each side of an equation produces an equivalent equation. Additive Inverse: Two numbers that when added together equal 0. Example, 3.2 and -3.2 Algebraic Expression: A mathematical phrase involving at least one variable. Expressions can contain numbers and operation symbols. Equation: A mathematical sentence that contains an equals sign. Evaluate an Algebraic Expression: To perform operations to obtain a single number or value. Inequality: A mathematical sentence that contains the symbols >,<,≥,or ≤. Inverse Operation: Pairs of operations that undo each other. Examples: Addition and subtraction are inverse operations and multiplication and division are inverse operations. Like Terms: Monomials that have the same variable raised to the same power. In other words, only coefficients of terms can be different. Linear Equation in One Variable: an equation that can be written in the form ax + b = c where a, b, and c are real numbers and a 0 Multiplication Property of Equality: For real numbers a, b, and c (c ≠0),if a +b,then ac =bc.In other words,multiplying both sides of an equation by the same number produces an equivalent expression. Multiplicative Inverses: Two numbers that when multiplied together equal 1. Example: 4 and ¼. Solution: the value or values of a variable that make an equation a true statement Solve: Identify the value that when substituted for the variable makes the equation a true statement. Variable: A letter or symbol used to represent a number. Math 8 Unit 3 Equal or Not Symbols absolute value bars < Less than Less than or equal to > Greater than Greater than or equal to Example 1 In front of a new ride at the amusement park is a pole that is 160 cm tall. On the pole is a sign that says, “To ride this attraction, your height must be within 30 cm of the height of this pole, inclusive.” Let h be the height of a rider and express the message on the sign algebraically using an absolute value inequality and using a compound inequality. Example 2 Solve the following for x and graph the solution of the inequality on a number line: a. 7 + x 1 – 2x b. 8 – 3(x – 5) = 12 c. A = 1 h(x + b) 2 Key Example 1 Links: http://purplemath.com /modules/ineqlin.htm http://purplemath.c om/modules/solveli n.htm http://www.purple math.com/modules/ solveabs.htm http://regentsprep. org/Regents/math/ solvin/LSolvIn.htm |h – 160| 30 ; Example 2 a. 7 + x 1 – 2x 6 -3x -2 x or x -2 b. 8 – 3(x – 5) = 12 8 – 3x + 15 = 12 - 3x + 23 = 12 -3x = -11 11 2 3 x= 3 3 1 h(x + b) 2 2A = hx + hb 2A – hb = hx 2A hb x h c. A = www.ceismc.gatech. edu/csi Solutions: h 190 and h 130; this can be written as 130 h 190 -2