**Step 1 — Recall the three conditions for a pair of linear equations.**

| Condition | Nature of lines | Number of solutions | Type |
|---|---|---|---|
| $\dfrac{a_1}{a_2} \neq \dfrac{b_1}{b_2}$ | intersecting | unique solution | consistent (independent) |
| $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} \neq \dfrac{c_1}{c_2}$ | parallel | no solution | inconsistent |
| $\dfrac{a_1}{a_2} = \dfrac{b_1}{b_2} = \dfrac{c_1}{c_2}$ | coincident | infinitely many solutions | consistent and **dependent** |

**Step 2 — Identify "consistent and dependent".**
Dependent means the two equations represent the **same (coincident)** line, i.e. infinitely many solutions.

**Step 3 — Write the required condition.**
$$\frac{a_1}{a_2} = \frac{b_1}{b_2} = \frac{c_1}{c_2}$$

**Answer : (D)**