Which of these systems has no solution?

Explanation

1. 01

   Only a system with $|A| = 0$ can fail to have a unique solution; that rules out the last two, whose determinants are $5$ and $-2$.

2. 02

   $4x + 6y = 10$ is twice $2x + 3y = 5$: infinitely many solutions. But three times $x - 2y = 4$ is $3x - 6y = 12$, not 7, so that system contradicts itself.