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### Systems of Equations and Inequalities

 What is a system of equations?  It is a collection of two or more equations with the same solution (common point) to both equations. The solution to a system of equations is the common solution (common point) to both equations. When do we use a system of equations?  Typically, it used when there is more than one unknown quantity and you want a specific amount for each quantity. For more information on the concept of a system of equations, click here.2.3.1a Solve system of equations by graphingExplanation:Notes | AnnotatedKhan video: Solving linear systems by graphing (both equations in slope-intercept form; 8th grade)Khan video: Systems of equations with graphing: y=7/5x-5 & y=3/5x-1Khan video: Graphing systems of equations (both equations are in standard form; 8th grade)Khan video: How to solve a system of linear equations, both exactly and approximately (example)Practice Problems:2.3.1b Determine if a point is a solution to a given system of equationExplanation:Khan video: Testing a solution for a system of equationsPractice Problems:Khan exercise: Solutions of systems of equations2.3.1c Solve system of equations by substitutionExplanationNotes | AnnotatedKhan article: Substitution method review (systems of equations)Khan video: Example 2: Solving systems by substitution (one equation in slope-intercept form and one in standard; 8th grade)Khan video: Example 3: Solving systems by substitution (both equations in standard form; 8th grade)Khan video: The substitution method (one standard form and one equation is x =; 8th grade)Khan video: How to solve a system of linear equations with substitution (example)Khan video: Systems of equations word problems example: Nickles and quartersPractice Problems:Khan exercise: Systems of equations with substitutionWorksheet #1Worksheet #2Worksheet: STEMersion2.3.2a Solve system of equations by linear combination (elimination)ExplanationKhan article: Elimination method review (systems of linear equations)Khan video: Systems of equations with elimination: x-4y=-18 & -x+3y=11 (add straight down)Khan video: Addition elimination method 2 (multiply one equation)Khan video: Example 2: Solving systems by elimination (multiply one equation)Khan  video: Addition elimination method 3 (infinitely many solutions)Khan video: Example 3: Solving systems by elimination (infinitely many solutions with graphing)Khan video: How to solve a system of linear equations with elimination (basic example)Khan video: How to solve a system of linear equations with elimination (advanced example)Khan video: Systems of equations with elimination challengeOptional: Why can we subtract one equation from the other in a system of equations?Practice Problems:Khan: Systems of equations with elimination - two coefficients are oppositeKhan: Systems of equations with elimination challenge (honors only)Worksheet #1 | AnswersWorksheet #2 | AnswersWorksheet #3 | AnswersPurchase ExamView Test Bank 2.3.2b Solve system of equations by linear combination (elimination): Word ProblemsExplanationHonors Notes | AnnotatedKhan video: Systems of equations with elimination: Sum/difference of numbers Khan video: Systems of equations with elimination: TV & DVD Khan video: Systems of equations with elimination: apples and orangesWebsite article: Wind and Current ProblemsPractice Problems2.3.2c Systems of Equations with three variables (honors)ExplanationPractice:2.3.2d State the Number of Solutions to a system of equationsExplanation:Khan article: Number of solutions to system of equations reviewKhan video: Solving systems by graphing 3 (one equation in slope-intercept and the other needs to be changed; no solution)Khan video:  Solving systems by elimination 3 (and graphing)Khan video: Solving systems by substitution 1 (and graphing)Khan video: Example 1: Solving systems by substitution (no solution)Khan video: Substitution method 2 (no solution)Khan video:  Solving systems by graphing 2 (includes a no solution)Khan video: How to identify equivalent systems of equations (example)Khan video: How to identify non-equivalent systems of equations (example)Khan video: How to determine the number of solutions of a system of equations using algebraic reasoning (example)Practice Problems2.3.2e Equivalent Systems of Equations (honors)ExplanationPractice:Khan Practice: Equivalent systems of equations2.3.2f System of Equations Mixed ReviewExplanation:Khan video - Problem Solving Word Problems 2Practice Problems:One equation or a system of equations WSWorksheet #1 Worksheet #2Khan Practice - Solve any system of two linear equationsKhan Practice - Systems of equations word problems capstoneJeopardy style-online game with system of equations -  Reviews each method for solving system of equations2.3.3 Graphing Inequalities in Two VariablesExplanation:Khan Article: Graphing inequalities (x-y plane) reviewKhan Video: Intro to graphing two-variable inequalities (in slope-intercept form)Khan Video: Graphing two-variable inequalities (in slope-intercept form)Khan Video: Graphing inequalities 2 (in standard form) (old content)Khan Video: Two-variable inequalities from their graphs (given a graph, find the inequality)Khan Video: Testing solutions to inequalities (verify solutions)Khan video: Writing two-variable inequalities word problemKhan video: Solving two-variable inequalities word problemKhan video: Graphs of two-variable inequalities word problemPractice ProblemsKhan Exercise: Solutions of inequalities: algebraicKhan Exercise: Solutions of inequalities: graphicalKhan Exercise: Graphs of inequalities Khan Exercise: Two-variable inequalities from their graphsKhan Exercise: Two-variable inequalities word problemsDesmos Activity: Point Collector: LinesWorksheet #1Worksheet #22.3.4 Systems of linear inequalitiesExplanation:Khan Video: Intro to graphing systems of inequalitiesKhan video: Testing solutions for a system of inequalitiesKhan Video: Graphing systems of inequalities 2 (word problem)Khan video: Writing systems of inequalities word problemKhan video: Solving systems of inequalities word problemKhan video: Graphs of systems of inequalities word problemKhan Video: Graphing systems of inequalities (three inequalities)Practice Problems:Khan exercise: Testing solutions to systems of inequalitiesKhan exercise: Graphing and solving systems of inequalitiesKhan exercise: Systems of inequalities word problemsWorksheet #1Review