Question-25

Consider the following system of linear equations:

\[ \begin{aligned} x_1 - 3x_2 &= 4\\ 3x_1 + kx_2 &= -12 \end{aligned} \]

where \(k \in \mathbb{R}\). If the given system has a unique solution then \(k\) should not be equal to \(----\).

Answer

\(-9\)

Solution

For the system to have a unique solution we have:

\[ \frac{1}{3} \neq \frac{-3}{k} \Longrightarrow k\neq -9 \]