Back to Graph linear inequalities — Problem 4 · Task Set 54

Exercises: Graph Linear Inequalities and Systems

For each graphing problem, state: (1) whether the boundary is solid or dashed, (2) which test point you used, and (3) which half-plane is shaded. For systems, verify a point in the feasible region satisfies all inequalities.

Grade 9·18 problems·~40 min·Common Core Math - HS Algebra·standard·hsa-rei-d-12

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Fluency Practice

$Coordinate plane showing two solid boundary lines intersecting. The region above y = x minus 1 is shaded blue. The region below y = negative x plus 3 is shaded yellow. The overlap (intersection of both shadings) is shaded green, forming a triangular region.$

Describe how to graph the system $y \geq x - 1$ and $y \leq -x + 3$ , and find the solution region.

(a) Describe the boundary lines and which half-plane each inequality shades.
(b) Verify that $(1, 2)$ is in the solution region by checking both inequalities.