Lesson Worksheet: Solving Systems of Linear Inequalities Mathematics • 9th Grade

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In this worksheet, we will practice solving systems of linear inequalities by graphing them and identifying the regions representing the solution.

Q1:

Fill in the blank: The shaded area represents the solution set of the inequalities 𝑦≥3, 𝑥≥0, and .

  • A𝑦+2𝑥+8≤0
  • B2𝑦+𝑥−8≤0
  • C𝑦+2𝑥−8≤0
  • D2𝑦+𝑥+8≤0

Q2:

Which of the following points is a solution to the system of inequalities 𝑥≥0, 𝑦≥0, 3𝑥−4𝑦≥−8, and 𝑥+𝑦≥−9?

  • A(−1,0)
  • B(−9,8)
  • C(8,1)
  • D(−4,5)
  • E(−5,−2)

Q3:

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

Q4:

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

Q5:

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

  • A𝑥≥0, 𝑦≥0, 3≤𝑥≤6, 2≤𝑦<6, 𝑥+𝑦<8
  • B𝑥≥0, 𝑦≥0, 3≤𝑥<6, 2≤𝑦≤6, 𝑥+𝑦>8
  • C𝑥≥0, 𝑦≥0, 3≤𝑦<6, 2≤𝑥≤6, 𝑥+𝑦≤8
  • D𝑥≥0, 𝑦≥0, 3≤𝑥<6, 2≤𝑦≤6, 𝑥+𝑦≤8
  • E𝑥≥0, 𝑦≥0, 3≤𝑥≤6, 2≤𝑦≤6, 𝑥+𝑦≤8

Q6:

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

Q7:

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

Q8:

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

Q9:

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

  • AE
  • BG
  • CF
  • DA
  • ED

Q10:

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

  • AA
  • BF
  • CD
  • DE
  • EC

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