Solve the following system of equations.
\[
\left\{\begin{array}{l}
y=x^{2}-8 x+2 \\
y=-2 x+18
\end{array}\right.
\]
If there is more than one solution, use th

Step 1 ：The system of equations is composed of two equations, one quadratic and one linear.

Step 2 ：To find the solution, we need to set the two equations equal to each other and solve for x.

Step 3 ：Setting the equations equal to each other gives us \(x^{2} - 8x + 2 = -2x + 18\).

Step 4 ：Solving this equation gives us two solutions for x: \(-2\) and \(8\).

Step 5 ：We can then substitute these x values into one of the equations to find the corresponding y values.

Step 6 ：Substituting \(x = -2\) into the equation \(y = -2x + 18\) gives us \(y = 22\).

Step 7 ：Substituting \(x = 8\) into the same equation gives us \(y = 2\).

Step 8 ：Final Answer: The solutions to the system of equations are \(\boxed{(-2, 22)}\) and \(\boxed{(8, 2)}\).