Lesson Worksheet: Solution Cases of System of Linear Equations Mathematics • 9th Grade

In this worksheet, we will practice determining whether a linear system of equations has a unique solution, no solution, or an infinite number of solutions.

Q1:

Determine the number of solutions to the system of equations 6𝑥2𝑦+9𝑧=4,24𝑥8𝑦+36𝑧=22,12𝑥4𝑦+18𝑧=10.

  • AThere are no solutions.
  • BThere are finitely many solutions, not including 𝑥=0,𝑦=0,𝑧=0.
  • CThere are infinitely many solutions.
  • DThe only solution is 𝑥=0,𝑦=0,𝑧=0.

Q2:

Determine the number of solutions to the following system: 4801301101417𝑥𝑦𝑧=000.

  • AThere are infinitely many solutions.
  • BThere are finitely many solutions, not including 𝑥=0,𝑦=0,𝑧=0.
  • CThe only solution is 𝑥=0,𝑦=0,𝑧=0.
  • DThere are no solutions.

Q3:

Determine the value of 𝑘 that makes the system of equations 7𝑥+5𝑦=7,35𝑥+25𝑦=𝑘 have infinitely many solutions.

Q4:

Find the set of values of 𝑘 for which the simultaneous equations 9𝑥9𝑦5𝑧=6,2𝑥+3𝑦+7𝑧=4,3𝑥4𝑦+𝑘𝑧=7, have at least one solution.

  • A14845
  • B2245
  • C2245
  • D43645
  • E14845

Q5:

If 𝑏0 and 𝐴 is an invertible 𝑛×𝑛 matrix, can the solution set of 𝐴𝑥=𝑏 be a plane through the origin?

  • ANo
  • BYes

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