Simultaneous equations and planesEdexcel A-Level Further Maths: Mind map

Exam questions on Simultaneous equations and planes

1. Three planes have equations $x+y+z=6$, $\ 2x-y+z=3$ and $x+2y-z=2$.
   Use the inverse of $\mathbf{M}$, found using your calculator, to solve the equations.2 marks
2. Three planes have equations $x+2y-z=4$, $\ 2x+y+z=5$ and $3x+3y=k$, where $k$ is a constant.
   Describe the geometrical configuration of the three planes when $k=6$, giving a reason.2 marks
3. Three planes have equations $\Pi_1:\ x+2y+3z=5$, $\ \Pi_2:\ 2x+4y+6z=7$ and $\Pi_3:\ x-y+z=1$.
   Explain why the equations have no solution, and describe the geometrical configuration of the three planes.3 marks