Question

If the pair of linear equations: a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 is consistent and dependent, then

विकल्प

• `(a_1)/(a_2) ≠ (b_1)/(b_2)`

• `(a_1)/(a_2) ≠ (b_1)/(b_2) = (c_1)/(c_2)`

• `(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)`

• `(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)`

Answer 1

`bb((a_1)/(a_2) ≠ (b_1)/(b_2) = (c_1)/(c_2))`

Explanation:

The three conditions for linear equations are:

1. Unique Solution: `(a_1)/(a_2) ≠ (b_1)/(b_2)` (Consistent and Independent).

2. No Solution: `(a_1)/(a_2) = (b_1)/(b_2) ≠ (c_1)/(c_2)` (Inconsistent).

3. Infinitely Many Solutions: `(a_1)/(a_2) = (b_1)/(b_2) = (c_1)/(c_2)` (Consistent and Dependent).

The question explicitly asks for the consistent and dependent case.

The condition is `(a_1)/(a_2) ≠ (b_1)/(b_2) = (c_1)/(c_2)`.