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Chapter 14: Simultaneous Equations (Three Unknowns) - Exercises

Solve the following systems of equations for \(x\), \(y\), and \(z\):

  1. \(\begin{cases} x + y + z = 6 \\ 2x - y + z = 3 \\ x + 2y - z = 2 \end{cases}\)
  2. \(\begin{cases} 3x + y - z = 4 \\ x + 2y + 2z = 11 \\ 2x - y + 3z = 9 \end{cases}\)
  3. \(\begin{cases} x + y = 5 \\ y + z = 7 \\ x + z = 6 \end{cases}\)

Answer Key

  1. \(x = 1, \; y = 2, \; z = 3\)
  2. \(x = 1, \; y = 3, \; z = 2\)
  3. \(x = 2, \; y = 3, \; z = 4\)