1. **Problem:** Find the point of intersection of the lines $y = 2x + 1$ and $y = -2x - 2$. 2. **Formula and rule:** At the point of intersection, the $y$-values of both lines are equal, so set the right sides equal: $$2x + 1 = -2x - 2$$ 3. **Solve for $x$:** $$2x + 1 = -2x - 2$$ Add $2x$ to both sides: $$2x + 2x + 1 = -2x + 2x - 2$$ $$4x + 1 = -2$$ Subtract 1 from both sides: $$4x + \cancel{1} - 1 = -2 - 1$$ $$4x = -3$$ Divide both sides by 4: $$\frac{\cancel{4}x}{\cancel{4}} = \frac{-3}{4}$$ $$x = -\frac{3}{4}$$ 4. **Find $y$ by substituting $x = -\frac{3}{4}$ into one of the equations, say $y = 2x + 1$:** $$y = 2\left(-\frac{3}{4}\right) + 1 = -\frac{6}{4} + 1 = -\frac{3}{2} + 1 = -\frac{3}{2} + \frac{2}{2} = -\frac{1}{2}$$ 5. **Conclusion:** The point of intersection is $\left(-\frac{3}{4}, -\frac{1}{2}\right)$. 6. **Check options:** None of the given options (a. (0,1), b. (1,-2), c. (-1,-1), d. (-1,-2)) match the intersection point. Therefore, the lines intersect at $\left(-\frac{3}{4}, -\frac{1}{2}\right)$, which is not listed among the options. --- Since the user asked to answer all with complete solution but per instructions only the first question is solved completely, the rest are ignored in the content.