Systems of Inequalities

Explore boundary lines, feasible region, checking points.

Lesson 4 of 53 parts Practice Flashcards

1/3

Boundary Lines

Objective: Explain boundary lines and use it to solve or interpret a problem.

Draw each equality boundary; use a solid line for inclusive inequalities and dashed for strict ones. Test a point to choose the correct side. When ≤ or ≥ is used.

Worked examples

Try itSystems of Inequalities — practice 1.1: For y≤4x+3, what is the largest allowed integer y at x=5?Show answer

Step 1: Substitute x=5: y≤23. Step 2: The boundary is included by ≤. Step 3: The largest allowed integer is 23.

Swipe sideways to move between sections

Boundary Lines

Objective: Explain boundary lines and use it to solve or interpret a problem.

Draw each equality boundary; use a solid line for inclusive inequalities and dashed for strict ones. Test a point to choose the correct side. When ≤ or ≥ is used.

Worked examples

Try itSystems of Inequalities — practice 1.1: For y≤4x+3, what is the largest allowed integer y at x=5?Show answer

Step 1: Substitute x=5: y≤23. Step 2: The boundary is included by ≤. Step 3: The largest allowed integer is 23.

Feasible Region

Objective: Explain feasible region and use it to solve or interpret a problem.

The solution to a system of inequalities is the intersection of all its half-planes, which can be bounded, unbounded, or empty. No, every constraint must hold.

Worked examples

Try itSystems of Inequalities — practice 2.1: For y≤2x+4, what is the largest allowed integer y at x=8?Show answer

Step 1: Substitute x=8: y≤20. Step 2: The boundary is included by ≤. Step 3: The largest allowed integer is 20.

Checking Points

Objective: Explain checking points and use it to solve or interpret a problem.

Substitute a candidate coordinate into every inequality; graph shading can be imprecise near boundaries. Strict signs exclude equality but inclusive signs allow it.

Worked examples

Try itSystems of Inequalities — practice 3.1: For y≤3x+5, what is the largest allowed integer y at x=11?Show answer

Step 1: Substitute x=11: y≤38. Step 2: The boundary is included by ≤. Step 3: The largest allowed integer is 38.

You finished the reading!

Lock it in with a few practice questions, then move on to the next lesson.

Practice Next lesson

Previous lessonSolving Systems with Matrices Next lessonLinear Optimization in Context