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Systems of equations practice

Graphing systems of inequalities worksheets

Graph eight pairs of linear inequalities, distinguish strict and inclusive boundaries, and shade each common solution region on a coordinate grid.

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Graph both boundaries, choose the correct side of each line and shade only the common region. Label the boundary intersection and note whether it is included.

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Two half-planes, one common region

Graph each boundary, use a dashed line for a strict inequality and a solid line when equality is included, then shade only the overlap. The boundary intersection is labeled separately because the full solution is a region.

Check a point inside the proposed overlap in both original inequalities. A strict boundary can make the boundary intersection itself excluded.

Learning objective

What this activity builds

Graph two linear inequalities and identify the points that satisfy both statements.

Worked example

Graph y ≤ x + 1 and y > −x − 1. Does (0, 0) belong to the common region?

Yes. Shade above the dashed line y = −x − 1 and on or below the solid line y = x + 1.

At (0, 0), 0 ≤ 1 and 0 > −1, so the point satisfies both inequalities. The common region is the overlap of the two half-planes, not only the boundary intersection.

Teaching notes

Make the practice count

  • Draw and label both boundary lines before shading.
  • Use a test point away from a boundary to choose each half-plane.
  • Keep strict boundaries dashed and inclusive boundaries solid.
  • Check the final overlap with a point inside the shaded region.

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Choose boundary forms. Student grids stay blank; answer editions show the exact common region, boundary styles and boundary intersection.

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Math SheetNameScore/ 8TeacherDateGraphing Systems of InequalitiesGraph both inequalities and shade their common solution region. Label the boundary intersection.1.-5-5-4-4-3-3-2-2-1-101122334455xy13x+2y-142x-2Boundary intersection:2.-5-5-4-4-3-3-2-2-1-101122334455xy1y-x+22y2Boundary intersection:3.-5-5-4-4-3-3-2-2-1-101122334455xy1y-35x+1752y-43x+193Boundary intersection:4.-5-5-4-4-3-3-2-2-1-101122334455xy17x-4y-2022x-y-5Boundary intersection:5.-5-5-4-4-3-3-2-2-1-101122334455xy1x-2y-125x-y-5Boundary intersection:6.-5-5-4-4-3-3-2-2-1-101122334455xy1y-14x+2142x1Boundary intersection:7.-5-5-4-4-3-3-2-2-1-101122334455xy1y8x-52y-72x-5Boundary intersection:8.-5-5-4-4-3-3-2-2-1-101122334455xy1x+4y82x-4Boundary intersection:math-sheet.comPage 1 / 1

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