Condition for a consistent pair of linear equations -

Consistent equations means the equations must have solution so lines may either coincide(with infinitely many solutions) or with a unique solution {lines must not be parallel}.

1) Must not be parallel so,

a₁/a₂ b₁/b₂ [intersecting lines with unique solution]

2) Also the lines can coincide, so,

a₁/a₂ = b₁/b₂ = c₁/c₂ [coincident or dependent]