Question

for the following simultaneous equations, k is a real constant:
kx-3y=k+3
4x+(k+7)y=1

Find the value of k for which there are infinitely many solutions.

Answer 1

\[\frac{k}{4} = \frac{-3}{k+7} = \frac{k+3}{1}\]

Answer 2

i dont understand this

Answer 3

Please, as @ParthKohli has suggested, you have to pick the common root of these three equations:
\[\begin{gathered}
\frac{k}{4} = \frac{{ - 3}}{{k + 7}} \hfill \\
\frac{k}{4} = k + 3 \hfill \\
\frac{{ - 3}}{{k + 7}} = k + 3 \hfill \\
\end{gathered} \]

Answer 4

\[
\begin{vmatrix}
k&-3\\
4x&k+7
\end{vmatrix}
=0
\]
The determinant must be zero as the equations have infinitely many solution. Not absolutely sure though. Check your notes.