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

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 𝑦β‰₯3, π‘₯β‰₯0, and .

  • A𝑦+2π‘₯+8≀0
  • B2𝑦+π‘₯βˆ’8≀0
  • C𝑦+2π‘₯βˆ’8≀0
  • D2𝑦+π‘₯+8≀0

Q2:

Which of the following points is a solution to the system of inequalities π‘₯β‰₯0, 𝑦β‰₯0, 3π‘₯βˆ’4𝑦β‰₯βˆ’8, and π‘₯+𝑦β‰₯βˆ’9?

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

Q3:

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

  • Aπ‘₯≀0, 𝑦β‰₯0
  • Bπ‘₯β‰₯0, 𝑦≀0
  • Cπ‘₯≀0, 𝑦≀0
  • Dπ‘₯β‰₯0, 𝑦β‰₯0

Q4:

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

  • A𝑦>βˆ’3π‘₯+3, 𝑦β‰₯3π‘₯βˆ’8
  • B𝑦β‰₯3π‘₯βˆ’3, 𝑦>βˆ’3π‘₯+8
  • C𝑦β‰₯3π‘₯+3, 𝑦<βˆ’3π‘₯βˆ’8
  • D𝑦<3π‘₯βˆ’3, π‘¦β‰€βˆ’3π‘₯+8
  • E𝑦β‰₯3π‘₯+3, 𝑦>βˆ’3π‘₯βˆ’8

Q5:

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

  • Aπ‘₯β‰₯0, 𝑦β‰₯0, 3≀π‘₯≀6, 2≀𝑦<6, π‘₯+𝑦<8
  • Bπ‘₯β‰₯0, 𝑦β‰₯0, 3≀π‘₯<6, 2≀𝑦≀6, π‘₯+𝑦>8
  • Cπ‘₯β‰₯0, 𝑦β‰₯0, 3≀𝑦<6, 2≀π‘₯≀6, π‘₯+𝑦≀8
  • Dπ‘₯β‰₯0, 𝑦β‰₯0, 3≀π‘₯<6, 2≀𝑦≀6, π‘₯+𝑦≀8
  • Eπ‘₯β‰₯0, 𝑦β‰₯0, 3≀π‘₯≀6, 2≀𝑦≀6, π‘₯+𝑦≀8

Q6:

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

  • A𝑦<2π‘₯+6,π‘¦β‰€βˆ’π‘₯,π‘¦β‰€βˆ’10π‘₯+18
  • B𝑦<2π‘₯+6,𝑦β‰₯βˆ’π‘₯,𝑦β‰₯βˆ’10π‘₯+18
  • C𝑦<2π‘₯+6,𝑦β‰₯βˆ’π‘₯,π‘¦β‰€βˆ’10π‘₯+18
  • D𝑦<2π‘₯+6,𝑦β‰₯βˆ’π‘₯,𝑦≀10π‘₯+18
  • E𝑦>2π‘₯+6,𝑦β‰₯βˆ’π‘₯,π‘¦β‰€βˆ’10π‘₯+18

Q7:

Which of the regions on the graph contain solutions to the inequality 𝑦β‰₯2π‘₯βˆ’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<π‘₯,𝑦β‰₯2π‘₯βˆ’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>π‘₯,𝑦≀2π‘₯βˆ’4?

  • AE
  • BG
  • CF
  • DA
  • ED

Q10:

Which region on the graph contains solutions to the set of inequalities 𝑦>2,𝑦β‰₯βˆ’π‘₯,π‘₯<1?

  • AA
  • BF
  • CD
  • DE
  • EC

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