The pair of linear equations $kx + 3y+ 1 = 0$ and $2x + y + 3 = 0$ intersect each other, if
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → $k ≠ 6$
Step 1: Condition for intersection
Two lines:
$a_1x + b_1y + c_1 = 0 \quad \text{and} \quad a_2x + b_2y + c_2 = 0$
- They intersect if they are not parallel:
$\frac{a_1}{a_2} \ne \frac{b_1}{b_2}$
Step 2: Apply to given lines
- Line 1: $a_1 = k, b_1 = 3, c_1 = 1$
- Line 2: $a_2 = 2, b_2 = 1, c_2 = 3$
Parallel condition:
$\frac{k}{2} = \frac{3}{1} ⇒k = 6$
So, lines are parallel if k = 6.
Hence, lines intersect if:
$k \ne 6$