The system of equations
\(x + ky = 0\)
\(3x + 5y = 0\)
has infinitely many solutions, then \(k\) is equal to
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \(\displaystyle\frac{5}{3}\)
A homogeneous system always has the solution \(x = y = 0\). It has infinitely many solutions exactly when the determinant of the coefficients is zero.
\( \displaystyle \begin{vmatrix}1 & k\\3 & 5\end{vmatrix} = 0 \)
\(5 - 3k = 0\)
\( \displaystyle k = \frac{5}{3} \)