The pair of linear equations mx + 2y + 3 = 0 and 3x+6y+2 = 0 intersec…

The correct answer is Option (4) → $m≠1$

For two linear equations to intersect, their slopes must be different.

Given equations:

1. $mx + 2y + 3 = 0$
2. $3x + 6y + 2 = 0$

Find slopes

Equation (1):

$2y = -mx - 3 \Rightarrow y = -\frac{m}{2}x - \frac{3}{2}$

Slope = $-\frac{m}{2}$​

Equation (2):

$6y = -3x - 2 \Rightarrow y = -\frac{1}{2}x - \frac{1}{3}$

Slope = $-\frac{1}{2}$​

Condition for intersection:

$-\frac{m}{2} \neq -\frac{1}{2} \Rightarrow m \neq 1$