Number of solutions of linear equations

Consider the two equations

a₁x+b₁y=c₁

a₂x+b₂y=c₂

Then,

ü If a₁/a₂ = b₁/b₂ = c₁/c₂, then we have infinite solutions for these equations.

ü If a₁/a₂ = b₁/b₂ <> c₁/c₂, then we have no solution.

ü If a₁/a₂ <> b₁/b₂, then we have a unique solution.