1. **Problem:** Find the intersection point of the lines $y=3x+1$ and $y=-x-3$. 2. **Formula and rules:** To find the intersection, set the two equations equal: $$3x+1 = -x-3$$ 3. **Solve for $x$:** $$3x + 1 = -x - 3$$ $$3x + x = -3 - 1$$ $$4x = -4$$ $$x = \frac{\cancel{4}x}{\cancel{4}} = \frac{-4}{4} = -1$$ 4. **Find $y$ by substituting $x=-1$ into one of the equations:** $$y = 3(-1) + 1 = -3 + 1 = -2$$ 5. **Answer:** The lines intersect at the point $(-1, -2)$.