Question

If the system of equations
$3x+y=1$
$(2k-1)x+(k-1)y=2k+1$ is inconsistent, then $k=$

• A. $1$
• B. $-1$
• C. $-2$
• D. $2$

Answer 1

The correct option is D $2$

The system of equations is inconsistent if

$\frac{a_1}{a_2}=\frac{b_1}{b_2}\ne \frac{c_1}{c_2}$

$\therefore$ $\frac{3}{2k-1}=\frac{1}{k-1}\ne \frac{1}{2k+1}$
$\Rightarrow 3k-3=2k-1$
$\Rightarrow k=2$