Question

If the system of equations $ax+y=3,x+2y=3$ and $3x+4y=7$ is consistent, then value of $a$ is

• A. $2$
• B. $1$
• C. $-1$
• D. $0$

Answer 1

The correct option is A $2$

For the system of equations to be consistent:
$\Delta =0$
$\Rightarrow \Delta =\left|\begin{array}{ccc}a& 1& 3\\ 1& 2& 3\\ 3& 4& 7\end{array}\right|=0$

$R_1\to 2R_1-R_2$
$=\left|\begin{array}{ccc}2a-1& 0& 3\\ 1& 2& 3\\ 3& 4& 7\end{array}\right|$

$R_2\to 2R_2-R_3$
$=\left|\begin{array}{ccc}2a-1& 0& 3\\ -1& 0& -1\\ 3& 4& 7\end{array}\right|$
Expand using $C_2$
$=(2a-4)\left(4\right)=0$
$\Rightarrow a=2$