CC.2.2.HS.D.10

Represent, solve, and interpret equations/inequalities and systems of equations/inequalities algebraically and graphically.

Example Problems

Graph:

x + 5y = 5

Graph:

x - 2y = 6

Graph:

-8x - y = 8

Khan Academy Resources

Understanding the quadratic formula Solving quadratics by completing the square Solving quadratics by factoring review Intro to slope-intercept form Completing the square review Solving simple quadratics review Elimination method review (systems of linear equations)Graphing inequalities (x-y plane) review Number of solutions to system of equations review Substitution method review (systems of equations)Solving quadratics by taking square roots Compound inequalities review Solving quadratics by factoring Two-variable inequalities from their graphs Age word problems Quadratic formula Compound inequalities Using units to solve problems Quadratics by factoring (intro)Systems of equations with graphing Completing the square (intermediate)Completing the square Solutions to 2-variable equations Graphs of inequalities Systems of equations with substitution Systems of inequalities graphs Systems of equations with elimination Systems of equations with elimination challenge Quadratics by factoring Quadratics by taking square roots Slope-intercept intro Intercepts from a graph Quadratic word problems (standard form)Interpret points relative to a system Elimination strategies Solve equations by completing the square Systems of equations word problems Interpret quadratic models Solve equations using structure Solutions of inequalities: algebraic Number of solutions to a system of equations graphically Using inequalities to solve problems Creating systems in context Quadratics by taking square roots (intro)Systems of equations word problems (with zero and infinite solutions)Reasoning with systems of equations Solutions of systems of inequalities Features of quadratic functions Number of solutions to a system of equations algebraically Complete solutions to 2-variable equations Combining equations Comparing linear rates word problems Construct exponential models Quadratics by taking square roots: strategy Solutions of systems of equations Zero product property Strategy in solving quadratics Modeling with sinusoidal functions Systems of inequalities word problems Systems 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-1 Systems of equations with elimination: x-4y=-18 & -x+3y=11 Systems of equations with elimination: King's cupcakes Systems of equations with elimination: potato chips Systems of equations with substitution: potato chips Systems of equations number of solutions: fruit prices (1 of 2)Number of solutions to a system of equations graphically Systems of equations with substitution: -3x-4y=-2 & y=2x-5 Systems of equations number of solutions: fruit prices (2 of 2)Age word problem: Ben & William Age word problem: Arman & Diya Age word problem: Imran Inequalities with variables on both sides (with parentheses)Compound inequalities: OR Compound inequalities: AND A compound inequality with no solution Quadratic equations word problem: triangle dimensions Quadratic word problem: ball Worked example: completing the square (leading coefficient ≠ 1)Worked example: quadratic formula (negative coefficients)Solving quadratics by taking square roots Double inequalities Inequalities with variables on both sides Using units to solve problems: Drug dosage Compound inequalities examples Intro to graphing two-variable inequalities Systems of equations with elimination (and manipulation)Completing the square The quadratic formula Modeling with systems of inequalities Intercepts from an equation Two-variable inequalities from their graphs Number of solutions to a system of equations Systems of equations with elimination: TV & DVD Graphing systems of inequalities Solving quadratics by factoring Quadratic equations word problem: box dimensions Worked example: Completing the square (intro)Solving quadratics by completing the square: no solution Finding the vertex of a parabola in standard form Worked example: quadratic formula (example 2)Using the quadratic formula: number of solutions Testing a solution to a system of equations Solutions to systems of equations: consistent vs. inconsistent Intro to graphing systems of inequalities Systems of equations with substitution: coins Multi-step inequalities Solutions to systems of equations: dependent vs. independent Constructing exponential models: percent change Trig word problem: modeling annual temperature Constructing exponential models: half life Interpret quadratic models: Factored form Solve by completing the square: Non-integer solutions How many solutions does a system of linear equations have if there are at least two?Solving quadratics using structure Interpreting points in context of graphs of systems Solve by completing the square: Integer solutions Zero product property Graphs of systems of inequalities word problem Worked example: solutions to 2-variable equations Systems of equations with elimination: coffee and croissants Comparing linear rates example Strategy in solving quadratic equations Completing solutions to 2-variable equations Solving quadratics by taking square roots examples Number of solutions to a system of equations algebraically Graphs of two-variable inequalities word problem Two-variable linear equations intro Elimination strategies System of equations word problem: infinite solutions Solving quadratics by taking square roots: with steps Intro to slope-intercept form Solutions to 2-variable equations Intro to intercepts Systems of equations with elimination: apples and oranges Solving quadratics by factoring: leading coefficient ≠ 1 System of equations word problem: no solution Intervals and interval notation Solving two-variable inequalities word problem System of equations word problem: walk & ride Constructing exponential models Solving systems of inequalities word problem Trig word problem: modeling daily temperature Using inequalities to solve problems Function notation word problem: beach Interpreting two-variable inequalities word problem Systems of equations with graphing: exact & approximate solutions Worked example: Rewriting & solving equations by completing the square

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