To solve the system of equations given by:
- \( y = -7x - 4 \)
- \( y = -4x + 2 \)
we can find the intersection point by setting the right-hand sides of the equations equal to each other:
\[ -7x - 4 = -4x + 2 \]
Next, let's solve for \( x \):
- Add \( 4x \) to both sides:
\[ -7x + 4x - 4 = 2 \] \[ -3x - 4 = 2 \]
- Now, add \( 4 \) to both sides:
\[ -3x = 2 + 4 \] \[ -3x = 6 \]
- Divide both sides by \( -3 \):
\[ x = -2 \]
Now that we have \( x \), we can substitute it back into one of the original equations to find \( y \). We'll use the second equation:
\[ y = -4(-2) + 2 \] \[ y = 8 + 2 \] \[ y = 10 \]
Thus, the solution to the system of equations is:
\[ (x, y) = (-2, 10) \]
So the point of intersection is \((-2, 10)\).