Inconsistent linear systems (ACT/SAT/PSAT 8/9/10). Game on.

Both equations have slope $2$ but different $y$-intercepts ($3$ and $-1$), so the lines are parallel and the system has no solution.

Both equations have slope $-3$ but different $y$-intercepts ($2$ and $5$), so the lines are parallel and the system has no solution.

Both equations have slope $4$ but different $y$-intercepts ($-1$ and $3$), so the lines are parallel and the system has no solution.

Both equations have slope $-1$ but different $y$-intercepts ($6$ and $-2$), so the lines are parallel and the system has no solution.

Both equations have slope $6$ but different $y$-intercepts ($1$ and $-4$), so the lines are parallel and the system has no solution.

The first equation simplifies to $y = -5x + 6\textsf{,}$ and the second simplifies to $y = -\dfrac{10}{m}x + \dfrac{11}{m}\textsf{.}$ When $m = 2\textsf{,}$ $-\dfrac{10}{m} = -5\textsf{,}$ so the lines have the same slope, and since $6$ does not equal $\dfrac{11}{2}\textsf{,}$ the lines are parallel with different $y$-intercepts, so the system has no solution.

The first equation simplifies to $y = \dfrac{3}{2}x - \dfrac{1}{6}\textsf{,}$ and the second simplifies to $y = \dfrac{3}{k}x - \dfrac{5}{k}\textsf{.}$ When $k = 2\textsf{,}$ both slopes are $\dfrac{3}{2}\textsf{,}$ and since $-\dfrac{1}{6}$ does not equal $-\dfrac{5}{2}\textsf{,}$ the lines are parallel with different $y$-intercepts, so the system has no solution.

The first equation gives $y = -2x + 5\textsf{.}$ The second simplifies to $y = -2x + 6\textsf{,}$ so the slopes match but the intercepts differ and the system has no solution.