Chapter 13: Simultaneous Equations - Exercises

Solve the following systems of simultaneous linear equations for \(x\) and \(y\):

  1. \(\begin{cases} 2x + y = 13 \\ x - y = 2 \end{cases}\)
  2. \(\begin{cases} 3x + 4y = 18 \\ 2x - y = 1 \end{cases}\)
  3. \(\begin{cases} 5x - 2y = 11 \\ 3x + 2y = 13 \end{cases}\)
  4. \(\begin{cases} \frac{x}{2} + \frac{y}{3} = 5 \\ x - y = 0 \end{cases}\)
  5. \(\begin{cases} 4x + 3y = 25 \\ 5x - 2y = 14 \end{cases}\)

Answer Key

  1. \(x = 5, \; y = 3\)
  2. \(x = 2, \; y = 3\)
  3. \(x = 3, \; y = 2\)
  4. \(x = 6, \; y = 6\)
  5. \(x = 4, \; y = 3\)