Florida B.E.S.T. MA.912.AR.9.5

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 inequalities.

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

Teacher's field guide

What Students Need to Do: Students graph the boundary line for each inequality and decide whether each line is solid or dashed. They shade each half-plane and identify the region where the shading overlaps.
What Mastery Looks Like: Students draw each boundary line correctly and choose solid or dashed lines based on the inequality symbols. They shade the common region and test a point to confirm it satisfies both inequalities.
Common Misconceptions: Students may use a solid line for a strict inequality or a dashed line when equality is included. They may shade the wrong side or identify the union instead of the overlapping region.
How to Assess It: Give students y > 2x - 1 and y ≤ -x + 5. Ask them to graph the system and verify whether (1, 2) is a solution.

Lesson moves

Graph two inequalities on separate transparent sheets, then overlay them to reveal the solution region.
Ask students to explain in writing why a point inside one shaded region may not solve the system.
Use a card sort matching systems of inequalities, boundary line types, shaded graphs, and sample solution points.
Model ticket and snack limits with two inequalities, then graph the combinations that stay within a set budget.

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