AR.3.TM.2
Use concepts of systems of equations and inequalities (e.g., tables, graphs, matrix operations, pictorial representations, or algebraic properties) to model and solve real-world scenarios (e.g., compare ‘best deal opportunities’ with profit and expenses in businesses)
Example Problems
Candace purchased 2 notebooks and 3 pencils for a total of $9.
A month later, she purchased 3 notebooks and 2 pencils at the same prices, for a total of $8.
How much does one notebook cost?
A month later, she purchased 3 notebooks and 2 pencils at the same prices, for a total of $8.
How much does one notebook cost?
Erin bought 3 notebooks and 5 packs of pencils for a total of $15.
A month later, she bought 4 notebooks and 4 packs of pencils at the same prices, for a total of $14.
How much does a pack of pencils cost?
A month later, she bought 4 notebooks and 4 packs of pencils at the same prices, for a total of $14.
How much does a pack of pencils cost?
Natalie purchased 4 notebooks and 7 pens for a total of $22.
Another time, she purchased 5 notebooks and 5 pens (at the same prices) for a total of $20.
How much does one notebook cost?
Another time, she purchased 5 notebooks and 5 pens (at the same prices) for a total of $20.
How much does one notebook cost?
Khan Academy ResourcesElimination method review (systems of linear equations)Substitution method review (systems of equations)Age word problemsSystems of equations with graphingSystems of equations with substitutionSystems of inequalities graphsSystems of equations with eliminationSystems of equations with elimination challengeInterpret points relative to a systemElimination strategiesSystems of equations word problemsSolutions of inequalities: algebraicCreating systems in contextSystems of equations word problems (with zero and infinite solutions)Reasoning with systems of equationsSolutions of systems of inequalitiesCombining equationsSolutions of systems of equationsSystems of inequalities word problemsSystems of equations: trolls, tolls (2 of 2)Systems of equations: trolls, tolls (1 of 2)Systems of equations with graphing: y=7/5x-5 & y=3/5x-1Systems of equations with elimination: x-4y=-18 & -x+3y=11Systems of equations with elimination: King's cupcakesSystems of equations with elimination: potato chipsSystems of equations with substitution: potato chipsSystems of equations with substitution: -3x-4y=-2 & y=2x-5Age word problem: Ben & WilliamAge word problem: Arman & DiyaAge word problem: ImranSystems of equations with elimination (and manipulation)Systems of equations with elimination: TV & DVDGraphing systems of inequalitiesTesting a solution to a system of equationsSystems of equations with substitution: coinsSetting up a system of equations from context example (pet weights)Exponential vs. linear growth over timeInterpreting points in context of graphs of systemsGraphs of systems of inequalities word problemSystems of equations with elimination: coffee and croissantsSetting up a system of linear equations example (weight and price)Elimination strategiesSystem of equations word problem: infinite solutionsSystems of equations with elimination: apples and orangesSystem of equations word problem: no solutionSolving two-variable inequalities word problemSystem of equations word problem: walk & rideSolving systems of inequalities word problemSystems of equations with graphing: exact & approximate solutions
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