Clay graphed the following system of linear equations on a coordinate grid.
\[
\begin{array}{l}
y=-\frac{2}{3} x+2 \\
y=x-8
\end{array}
\]

What ordered pair represents the solution to this system of linear equatio

Step 1 ：Clay graphed the following system of linear equations on a coordinate grid: \(y=-\frac{2}{3} x+2\) and \(y=x-8\).

Step 2 ：The solution to a system of linear equations is the point where the two lines intersect. To find this point, we can set the two equations equal to each other and solve for x.

Step 3 ：Once we have the x-coordinate, we can substitute it into either of the original equations to find the corresponding y-coordinate.

Step 4 ：By solving the equations, we find that the solution is \(x = 6\) and \(y = -2\).

Step 5 ：The solution to the system of equations is the ordered pair (6, -2). This is the point where the two lines intersect on the graph.

Step 6 ：Final Answer: The solution to the system of equations is \(\boxed{(6, -2)}\).