Find all solutions of the system of equations algebraically. Write your solutions as coordinate points.
\[
\begin{array}{c}
y=-x^{2}-3 x+16 \\
2 x+y=10
\end{array}
\]

Step 1 ：The system of equations is given by two equations. The first equation is a quadratic equation and the second one is a linear equation.

Step 2 ：To find the solutions of the system, we can substitute the expression for y from the second equation into the first equation. This will give us a quadratic equation in terms of x.

Step 3 ：We can then solve this quadratic equation to find the values of x. Once we have the values of x, we can substitute them back into the second equation to find the corresponding values of y.

Step 4 ：The solutions for x are -3 and 2.

Step 5 ：Substituting these values into the second equation, we find the corresponding y values to be 16 and 6 respectively.

Step 6 ：Final Answer: The solutions of the system of equations are \(\boxed{(-3, 16)}\) and \(\boxed{(2, 6)}\).