For each ordered pair, determine whether it is a solution to the system of equations.
\[
\left\{\begin{array}{c}
y=2 x+1 \\
-5 x+3 y=8
\end{array}\right.
\]
\begin{tabular}{|c|c|c|}
\hline \multirow{2}{*}{$(x, y)$} & \multicolumn{2}{|c|}{ Is it a solution? } \\
\cline { 2 - 3 } & Yes & No \\
\hline$(0,1)$ & 0 & 0 \\
\hline$(3,-2)$ & 0 & 0 \\
\hline$(5,11)$ & 0 & 0 \\
\hline$(-7,-9)$ & 0 & 0 \\
\hline
\end{tabular}

Step 1 ：Given the system of equations: \[\left\{\begin{array}{c} y=2 x+1 \\ -5 x+3 y=8 \end{array}\right.\]

Step 2 ：We are given the ordered pairs (0,1), (3,-2), (5,11), and (-7,-9). We need to determine if these pairs are solutions to the system of equations.

Step 3 ：Substitute each pair of (x, y) into the two equations and check if both equations hold true.

Step 4 ：For the pair (0,1), substituting into the equations we get 1=2*0+1 which is true and -5*0+3*1=8 which is false. Therefore, (0,1) is not a solution.

Step 5 ：For the pair (3,-2), substituting into the equations we get -2=2*3+1 which is false and -5*3+3*(-2)=8 which is also false. Therefore, (3,-2) is not a solution.

Step 6 ：For the pair (5,11), substituting into the equations we get 11=2*5+1 which is true and -5*5+3*11=8 which is also true. Therefore, (5,11) is a solution.

Step 7 ：For the pair (-7,-9), substituting into the equations we get -9=2*(-7)+1 which is false and -5*(-7)+3*(-9)=8 which is also false. Therefore, (-7,-9) is not a solution.

Step 8 ：Final Answer: The only solution to the system of equations among the given ordered pairs is \(\boxed{(5,11)}\).