Question

For which value of k does the system have no solutions?

Answer 1

Given:

$\begin{gathered} 4x+y=3 \\ kx+y=-2 \end{gathered}$

To find the k value which the system has no solutions:

If the system has no solution, then

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

So, we get

$\begin{gathered} \frac{4}{k}=\frac{1}{1}\ne\frac{-3}{2} \\ \therefore k=4 \end{gathered}$

Hence, the answer is k=4.