Lesson Worksheet: Solving Systems of Linear Inequalities by Graphing Mathematics

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In this worksheet, we will practice solving systems of linear inequalities by graphing them and determining the region of the solution.

Q1:

Which region on the graph contains solutions to the set of inequalities 𝑦>2,𝑦≥−𝑥,𝑥<1?

  • AA
  • BF
  • CD
  • DE
  • EC

Q2:

Which region on the graph contains solutions to the set of inequalities 𝑦>𝑥,𝑦≤2𝑥−4?

  • AE
  • BG
  • CF
  • DA
  • ED

Q3:

Which regions on the graph contain solutions that satisfy both of the inequalities 𝑦<𝑥,𝑦≥2𝑥−4?

  • AA and B
  • BD and E
  • CC and F
  • DC and D
  • EE and F

Q4:

Which of the regions on the graph contain solutions to the inequality 𝑦≥2𝑥−4?

  • AA, B, C, and D
  • BA, B, D, and G
  • CA, D, E, and G
  • DA, B, D, and F
  • EC, D, E, and F

Q5:

Find the system of inequalities that forms the triangle shown in the graph.

  • A𝑦<2𝑥+6,𝑦≤−𝑥,𝑦≤−10𝑥+18
  • B𝑦<2𝑥+6,𝑦≥−𝑥,𝑦≥−10𝑥+18
  • C𝑦<2𝑥+6,𝑦≥−𝑥,𝑦≤−10𝑥+18
  • D𝑦<2𝑥+6,𝑦≥−𝑥,𝑦≤10𝑥+18
  • E𝑦>2𝑥+6,𝑦≥−𝑥,𝑦≤−10𝑥+18

Q6:

State the system of inequalities whose solution is represented by the following graph.

  • A𝑦>−3𝑥+3, 𝑦≥3𝑥−8
  • B𝑦≥3𝑥−3, 𝑦>−3𝑥+8
  • C𝑦≥3𝑥+3, 𝑦<−3𝑥−8
  • D𝑦<3𝑥−3, 𝑦≤−3𝑥+8
  • E𝑦≥3𝑥+3, 𝑦>−3𝑥−8

Q7:

State the system of inequalities whose solution is represented by the following graph.

  • A𝑥≤0, 𝑦≥0
  • B𝑥≥0, 𝑦≤0
  • C𝑥≤0, 𝑦≤0
  • D𝑥≥0, 𝑦≥0

Q8:

Find the solution set of the linear inequalities shown below.

  • A𝑦<−0.5𝑥−5
  • B∅
  • Cℝ
  • D𝑦>−0.5𝑥

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