Solve the following system of equations.
$$\{\begin{array}{l}y=x^2-8x+2\\ y=-2x+18\end{array}$$
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 $\boxed{{\displaystyle (-2,22)}}$ and $\boxed{{\displaystyle (8,2)}}$.