Florida B.E.S.T. MA.912.AR.9.3
The Standard
Given a mathematical or real-world context, solve a system consisting of two-variable linear or non-linear equations algebraically or graphically.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students find ordered pairs that make both equations true. They solve with algebra or locate intersections on a graph, then check and interpret every solution in the given situation.
What Mastery Looks Like
- Students choose substitution, elimination, or graphing based on the equations. They find every solution, check each ordered pair in both equations, and explain what the intersections mean in context.
Common Misconceptions
- Students may solve each equation separately instead of finding values that satisfy both. They may miss a second intersection, mistake a near intersection for a solution, or keep extraneous values created during algebraic work.
How to Assess It
- Give the exit ticket: “Solve y = x² and y = 2x + 3 algebraically. List both ordered pairs, then explain how a graph confirms them.”
Lesson moves
Ways to Teach It
Graph y = x² and y = 2x + 3 on transparencies, overlay them, then record and verify both intersection points.
Ask, “Why can a line and parabola have zero, one, or two solutions?” Students sketch examples and explain.
Run a card match with equation systems, graphs, solution sets, and labels for no solution, one solution, or multiple solutions.
Give h = -16t² + 48t + 5 and h = 21, then have students find when a ball reaches the platform.
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Printable MA.912.AR.9.3 Worksheet
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Related Standards
- MA.912.AR.9.9
Given a mathematical or real-world context, solve a system of three-variable linear equations algebraically.
- MA.912.AR.9.1
Given a mathematical or real-world context, write and solve a system of two-variable linear equations algebraically or graphically.
- MA.912.AR.9.2
Given a mathematical or real-world context, solve a system consisting of a two-variable linear equation and a non-linear equation algebraically or graphically.
- MA.8.AR.4.3
Given a mathematical or real-world context, solve systems of two linear equations by graphing.
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