Question

For what value of \( k \), does the system of equations \( x + 2y = 3 \) and \( 5x + ky = 15 \) have infinite solutions?

• A. \( 5 \)
• B. \( 10 \)
• C. \( 6 \)
• D. \( 12 \)

Hint:

A system has infinite solutions when the two equations are scalar multiples of each other.

Answer 1

The Correct Option is C

For infinite solutions, the two equations must be proportional:
\[ \frac{1}{5} = \frac{2}{k} = \frac{3}{15} \] Solving for \( k \):
\[ k = \frac{2 \times 15}{5} = 6. \]