Worksheet: Inconsistent Systems of Equations in Three Variables

In this worksheet, we will practice identifying inconsistent systems of equations in three variables.

Q1:

Find the set of values of 𝑘 for which the simultaneous equations have at least one solution.

  • A 2 2 4 5
  • B 1 4 8 4 5
  • C 2 2 4 5
  • D 1 4 8 4 5
  • E 4 3 6 4 5

Q2:

Find the value of 𝑘 that would make the equations 4 𝑥 + 9 𝑦 + 5 𝑧 = 0 , 1 6 𝑥 + 3 6 𝑦 + 𝑘 𝑧 = 0 , and 9 𝑥 8 𝑦 3 𝑧 = 0 have a solution other than zero.

Q3:

Three numbers add up to 216. The sum of the first two numbers is 112 and the third number is 8 less than this sum. How many possible values are there for the numbers?

  • A1
  • B0
  • Cinfinitely many

Q4:

Find the set of values of 𝑘 for which the simultaneous equations have at least one solution.

  • A 1 1 1
  • B 5
  • C 1 1 1
  • D { 5 }
  • E { 5 }

Q5:

Find the set of values of 𝑘 for which the simultaneous equations have at least one solution.

  • A 1 3 1 1 3
  • B 3 3 1 1 3
  • C 1 3 1 1 3
  • D 3 3 1 1 3
  • E 1 3 9 1 3

Q6:

Find the value of 𝑘 that would make the equations 5 𝑥 3 𝑦 + 9 𝑧 = 0 , 2 0 𝑥 1 2 𝑦 + 𝑘 𝑧 = 0 , and 2 𝑥 + 3 𝑦 + 3 𝑧 = 0 have a solution other than zero.

Q7:

Find the value of 𝑘 that would make the equations 6 𝑥 + 4 𝑦 + 3 𝑧 = 0 , 1 2 𝑥 + 8 𝑦 + 𝑘 𝑧 = 0 , and 8 𝑥 2 𝑦 4 𝑧 = 0 have a solution other than zero.

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