Question

If the system of equations
$x+2y-3=0$
$2x-y+4=0$
$\lambda x+y-3=0$ are consistent then the value of $\lambda$ is

• A. $1$
• B. $-1$
• C. $2$
• D. $-2$

Answer 1

The correct option is B $-1$

If three equations are consistent then the value of determinant formed by their coefficients is zero.
$\Rightarrow \left|\begin{array}{ccc}1& 2& -3\\ 2& -1& 4\\ \lambda & 1& -3\end{array}\right|=0$
$\Rightarrow 5+5\lambda =0$
$\Rightarrow \lambda =-1$