Florida B.E.S.T. MA.912.AR.9.4

MathGrades 9–12Write and solve a system of two- and three-variable equations and inequalities that describe quantities or relationships.

The Standard

Graph the solution set of a system of two-variable linear inequalities.

Florida B.E.S.T. Standards for Mathematics

Teacher's field guide

What Students Need to Do: Students graph each inequality on the same coordinate plane. They use solid or dashed boundary lines, shade each solution region, and identify the overlap.
What Mastery Looks Like: Students draw each boundary with the correct line type and shade the side that satisfies its inequality. They identify the overlap and verify points by substitution.
Common Misconceptions: Students often use a solid line for a strict inequality or a dashed line when equality is included. They may shade the wrong side or stop after shading only one inequality.
How to Assess It: Give students y > 2x - 1 and y ≤ -x + 5. Ask them to graph both and mark one point in the overlap.

Lesson moves

Graph two inequalities on transparency sheets, then stack them to reveal the overlapping solution region.
Ask students to explain how testing the point (0, 0) determines which side of a boundary to shade.
Play Match the Region using cards that show inequality systems, graphs, and points that satisfy both conditions.
Model a budget with limits on two purchases, then graph all combinations that meet the cost and quantity restrictions.

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