To solve the system of equations given by:
1. \( y = -3x - 5 \)
2. \( y = \frac{4}{3}x - 5 \)
we can set the two equations equal to each other since they both equal \( y \).
\[
-3x - 5 = \frac{4}{3}x - 5
\]
To eliminate the constant term \(-5\) from both sides, we can add 5 to both sides:
\[
-3x = \frac{4}{3}x
\]
Next, we want to eliminate the fraction by multiplying the entire equation by 3 to make calculations easier:
\[
3(-3x) = 3\left(\frac{4}{3}x\right)
\]
This simplifies to:
\[
-9x = 4x
\]
Next, we add \( 9x \) to both sides:
\[
0 = 4x + 9x
\]
This simplifies to:
\[
0 = 13x
\]
Now, we divide both sides by \( 13 \):
\[
x = 0
\]
Now, we substitute \( x = 0 \) back into one of the original equations to find \( y \). We can use either equation; let’s use the first one:
\[
y = -3(0) - 5
\]
This simplifies to:
\[
y = -5
\]
Thus, the solution to the system of equations is:
\[
(x, y) = (0, -5)
\]
Therefore, the point of intersection is \((0, -5)\).