The system x−2y+1=0, 2x+y−3=0x - 2y + 1 = 0,\; 2x + y - 3 = 0x−2y+ is —
Rewritten as x−2y=−1x - 2y = -1x−2y=−1 and 2x+y=32x + y = 32x+y=3, the ratio 12≠−21\dfrac{1}{2} \ne \dfrac{-2}{1}21=1−2, so the lines intersect at one point. The system is consistent and independent.