To solve the given system of equations, we have the following two equations:
- \( y = -5x - 8 \)
- \( y = \frac{2}{3}x - 8 \)
To find the points of intersection (the solution to the system), we can set the two equations equal to each other since both are equal to \(y\):
\[ -5x - 8 = \frac{2}{3}x - 8 \]
Next, simplify the equation. First, we can eliminate \(-8\) from both sides:
\[ -5x = \frac{2}{3}x \]
Now, to eliminate the fraction, multiply every term by 3:
\[ -15x = 2x \]
Next, we can add \(15x\) to both sides to isolate the \(x\) terms:
\[ 0 = 17x \]
Dividing by 17 gives us:
\[ x = 0 \]
Now that we have the value of \(x\), we can substitute it back into either of the original equations to find the corresponding \(y\)-coordinate. We'll use the first equation:
\[ y = -5(0) - 8 = -8 \]
Thus, the solution to the system of equations, which is the point of intersection, is:
\[ (x, y) = (0, -8) \]
Therefore, the final answer is:
\[ \boxed{(0, -8)} \]