Answer
Infinitely many solutions occur when the lines are identical (same slope $m_1 = m_2$ and same y-intercept $b_1 = b_2$). No solution occurs when the lines are parallel and distinct (same slope $m_1 = m_2$, but different y-intercepts $b_1 \ne b_2$).
Explanation
In standard form $A_1x + B_1y = C_1$ and $A_2x + B_2y = C_2$, infinitely many solutions mean $\frac{A_1}{A_2} = \frac{B_1}{B_2} = \frac{C_1}{C_2}$. No solution means $\frac{A_1}{A_2} = \frac{B_1}{B_2} \ne \frac{C_1}{C_2}$.