To solve the system of equations given by:
- \( y = -3x - 5 \)
- \( y = \frac{4}{3}x - 5 \)
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 \((0, -5)\).