Three planes have equations:

$2x-y+z=5$

$x+3y-z=4$     , where $a\text{, }b\in \mathbb{R}$.

$3x-5y+az=b$

Find the set of values of $a$ and $b$ such that the three planes have no points of intersection.

attempt to eliminate a variable (or attempt to find det $A$)       M1

  (or det $A=14\left(a-3\right)$)

(or two correct equations in two variables)       A1

  (or solving det $A=0$)

(or attempting to reduce to one variable, e.g. $\left(a-3\right)z=b-6$)       M1

$a=3\text{, }b\ne 6$       A1A1

[5 marks]