Solve the system of equations using technology:
\[
\begin{array}{l}
y=(4 x-1)^{2}-1 \\
y=-4 x+1
\end{array}
\]
Answer
\( \boxed{\text{Final Answer: } (\frac{1}{8} - \frac{\sqrt{5}}{8}, \frac{1}{2} + \frac{\sqrt{5}}{2}) \text{ and } (\frac{1}{8} + \frac{\sqrt{5}}{8}, \frac{1}{2} - \frac{\sqrt{5}}{2})} \)
Step 1 ：Set the two equations equal to each other: \( (4x - 1)^2 - 1 = -4x + 1 \)
Step 2 ：Solve for x: \( x = \frac{1}{8} - \frac{\sqrt{5}}{8} \) and \( x = \frac{1}{8} + \frac{\sqrt{5}}{8} \)
Step 3 ：Plug the x values back into either equation to find the corresponding y values: \( y = \frac{1}{2} + \frac{\sqrt{5}}{2} \) and \( y = \frac{1}{2} - \frac{\sqrt{5}}{2} \)
Step 4 ：\( \boxed{\text{Final Answer: } (\frac{1}{8} - \frac{\sqrt{5}}{8}, \frac{1}{2} + \frac{\sqrt{5}}{2}) \text{ and } (\frac{1}{8} + \frac{\sqrt{5}}{8}, \frac{1}{2} - \frac{\sqrt{5}}{2})} \)
