Question

The pair of equations 2x+3y= 5 and 6x+ky = 12 has no solution if k=

• A. 3
• B. 6
• C. 9
• D. 12

Answer 1

The Correct Option is C

To determine the condition for no solution in a pair of linear equations, the condition is: \[ \frac{a_1}{a_2} = \frac{b_1}{b_2} \neq \frac{c_1}{c_2} \] Given equations are: \[ 2x + 3y = 5 \quad \text{(1)} \\ 6x + ky = 12 \quad \text{(2)} \] Here: \[ a_1 = 2,\ a_2 = 6,\ b_1 = 3,\ b_2 = k,\ c_1 = 5,\ c_2 = 12 \] Now apply the condition: \[ \frac{a_1}{a_2} = \frac{2}{6} = \frac{1}{3}, \quad \frac{b_1}{b_2} = \frac{3}{k} \] For no solution: \[ \frac{1}{3} = \frac{3}{k} \Rightarrow k = 9 \]