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Lesson: Inconsistent Systems of Equations in Three Variables

Worksheet • 7 Questions

Q1:

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?

  • A0
  • Binfinitely many
  • C1

Q2:

Find the set of values of π‘˜ for which the simultaneous equations have at least one solution.

  • A ℝ βˆ’  βˆ’ 1 4 8 4 5 
  • B ℝ βˆ’  βˆ’ 4 3 6 4 5 
  • C βˆ’ 1 4 8 4 5
  • D ℝ βˆ’  βˆ’ 2 2 4 5 
  • E βˆ’ 2 2 4 5

Q3:

Find the set of values of π‘˜ for which the simultaneous equations have at least one solution.

  • A ℝ βˆ’ { βˆ’ 5 }
  • B ℝ βˆ’ { 5 }
  • C βˆ’ 5
  • D ℝ βˆ’  βˆ’ 1 1 1 
  • E βˆ’ 1 1 1

Q4:

Find the set of values of π‘˜ for which the simultaneous equations have at least one solution.

  • A ℝ βˆ’  βˆ’ 3 3 1 1 3 
  • B ℝ βˆ’  βˆ’ 1 3 9 1 3 
  • C βˆ’ 3 3 1 1 3
  • D ℝ βˆ’  1 3 1 1 3 
  • E 1 3 1 1 3

Q5:

Find the value of π‘˜ that would make the equations 4 π‘₯ + 9 𝑦 + 5 𝑧 = 0 , 1 6 π‘₯ + 3 6 𝑦 + π‘˜ 𝑧 = 0 , and 9 π‘₯ βˆ’ 8 𝑦 βˆ’ 3 𝑧 = 0 have a solution other than zero.

Q6:

Find the value of π‘˜ that would make the equations βˆ’ 5 π‘₯ βˆ’ 3 𝑦 + 9 𝑧 = 0 , βˆ’ 2 0 π‘₯ βˆ’ 1 2 𝑦 + π‘˜ 𝑧 = 0 , and 2 π‘₯ + 3 𝑦 + 3 𝑧 = 0 have a solution other than zero.

Q7:

Find the value of π‘˜ that would make the equations βˆ’ 6 π‘₯ + 4 𝑦 + 3 𝑧 = 0 , βˆ’ 1 2 π‘₯ + 8 𝑦 + π‘˜ 𝑧 = 0 , and βˆ’ 8 π‘₯ βˆ’ 2 𝑦 βˆ’ 4 𝑧 = 0 have a solution other than zero.

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