Question

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

Options

• `(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:

When two lines coincide (are dependent), they have infinitely many solutions. According to the mathematical rule, infinitely many solutions are possible only when the ratios of all the coefficients of both equations are equal.