The system $x - 2y + 1 = 0,\; 2x + y - 3 = 0$ is —

Rewritten as $x - 2y = -1$ and $2x + y = 3$, the ratio $\dfrac{1}{2} \ne \dfrac{-2}{1}$, so the lines intersect at one point. The system is consistent and independent.