Inconsistent linear systems practice

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.

Combine like terms in the first equation: $5x + y = 6$. Matching the $x$- and $y$-coefficient ratios with the second equation gives $m = 2$, so the lines are parallel. Multiplying the first equation by $2$ would require $12$ on the right of the second equation, not $11$, so the lines have different intercepts and there is no solution.

Combine like terms in the first equation: $9x - 6y = 1$. Matching the $x$- and $y$-coefficient ratios with the second equation gives $k = 2$, so the lines are parallel. Multiplying the first equation by $\dfrac{1}{3}$ would require $\dfrac{1}{3}$ on the right of the second equation, not $5$, so the lines have different intercepts and there is no solution.

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