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Cramer's rule solves a two-by-two system directly: x = (c₁b₂ − c₂b₁)/D and y = (a₁c₂ − a₂c₁)/D where D = a₁b₂ − a₂b₁. A zero determinant means the lines are parallel.
Cramer's rule
D = a₁b₂ − a₂b₁, x = (c₁b₂ − c₂b₁)/D, y = (a₁c₂ − a₂c₁)/D
D = −14, giving x = 3 and y = 2.
The two lines have the same gradient: either they never meet (no solution) or they coincide (infinitely many).