Question

If the pair of equations \( 3x + 4y = k \) and \( 9x + 12y = 6 \) has infinite number of solutions, then the value of k is:

• A. 1
• B. 2
• C. 3
• D. 4

Hint:

For the system of linear equations to have infinite solutions, the two equations must be proportional to each other.

Answer 1

The Correct Option is B

For the pair of equations to have infinite solutions, the second equation must be a scalar multiple of the first equation. \[ \frac{9x + 12y}{3x + 4y} = \frac{6}{k} \quad \text{(divide both equations by 3x + 4y)} \] Simplifying, we get: \[ \frac{9}{3} = \frac{6}{k} \quad \Rightarrow \quad 3 = \frac{6}{k} \quad \Rightarrow \quad k = 2. \]