At the intersection of the two lines, both equations have the same $y$-value. Since one line is $y=7$, substitute $7$ for $y$ in $y=2x+1$:

Subtract $1$ from both sides:

Then divide by $2$:

So the value of $x$ is $3$.

Since $y=7$ and $x+y=18$, substitute $7$ for $y$ in the first equation: $x+7=18$. Then subtract $7$ from both sides to get $x=11$.

The table says that selling $4$ student tickets and $6$ adult tickets brings in the same total amount as selling $7$ student tickets and $4$ adult tickets. Since one equation is

the total for the first combination is $50$. Therefore, the other combination must also total $50$, so

A solution to a system is an ordered pair that makes each equation in the system true. Since $(4,-1)$ is a solution, substituting $x=4$ and $y=-1$ must satisfy both equations.

The total number of vehicles is the number of cars plus the number of motorcycles, so $c+m=18$. Each car has $4$ wheels and each motorcycle has $2$ wheels, so the total number of wheels is $4c+2m=50$. Therefore, the correct system is $c+m=18$ and $4c+2m=50$.