CAIE Further Paper 2 2022 November — Question 2

Exam BoardCAIE
ModuleFurther Paper 2 (Further Paper 2)
Year2022
SessionNovember
TopicSimultaneous equations

2
  1. Show that the system of equations $$\begin{aligned} & x - y + 2 z = 4
    & x - y - 3 z = a
    & x - y + 7 z = 13 \end{aligned}$$ where \(a\) is a constant, does not have a unique solution.
  2. Given that \(a = - 5\), show that the system of equations in part (a) is consistent. Interpret this situation geometrically.
  3. Given instead that \(a \neq - 5\), show that the system of equations in part (a) is inconsistent. Interpret this situation geometrically.