Given two lines are: 2x - 3y = -5 and -4x + 6y = -10
Note: Two lines in the form a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0 are:
i) Said to be consistent and has an unique solution, if a₁/a₂ is not equal to b₁/b₂
ii) Said to be consistent and has infinitely many solutions, if a₁/a₂ = b₁/b₂ = c₁/c₂
iii) Said to be inconsistent, no solution and parallel, if a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Here in the given set, a₁/a₂ = 2/-4 = -1/2
b₁/b₂ = -3/6 = -1/2
c₁/c₂ = -5/-10 = 1/2
Thus we have a₁/a₂ = b₁/b₂ ≠ c₁/c₂
Hence, the two lines given by the equations have no solution; inconsistent and
parallel.