Find the value of $a$ for which the system of equations does not have a unique solution.

Find the solution of the system of equations when $a=2$.

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

an attempt at a valid method eg by inspection or row reduction       (M1)

$2\times R_2=R_1\Rightarrow 2a=-1$

$\Rightarrow a=-\frac{1}{2}$      A1

[2 marks]

using elimination or row reduction to eliminate one variable      (M1)

correct pair of equations in 2 variables, such as

$\begin{array}{c}5x+10y=25\\ 5x+12y=4\end{array}\}$      A1

Note: Award A1 for $z$ = 0 and one other equation in two variables.

attempting to solve for these two variables      (M1)

$x=26$,  $y=-10.5$,  $z=0$      A1A1

Note: Award A1A0 for only two correct values, and A0A0 for only one.

Note: Award marks in part (b) for equivalent steps seen in part (a).

[5 marks]