To solve the system of equations given by
- \( y = -3x \)
- \( y = 5x + 8 \)
we can set the two equations equal to each other because they both equal \( y \):
\[ -3x = 5x + 8 \]
Now, we'll solve for \( x \):
- Add \( 3x \) to both sides:
\[ 0 = 8x + 8 \]
- Subtract \( 8 \) from both sides:
\[ -8 = 8x \]
- Divide by \( 8 \):
\[ x = -1 \]
Now that we have the value of \( x \), we can substitute it back into either equation to find the corresponding \( y \)-value. We'll use the first equation:
\[ y = -3(-1) = 3 \]
Therefore, the solution to the system of equations, or the point of intersection, is
\[ (x, y) = (-1, 3) \]
So, the solution is \( (-1, 3) \).