https://file.aiquickdraw.com/mathbot/file/1728431735632nq9pzxmh.jpg

The image contains three systems of nonlinear equations labeled as **a**, **b**, and **c**, each with two equations. The task is to solve these systems using either the **substitution** or **elimination** method.

### a) 
\[
\begin{cases}
16x^2 - y^2 + 16y - 128 = 0 \quad \text{(1)} \\
y^2 - 48x - 16y - 32 = 0 \quad \text{(2)}
\end{cases}
\]

### b) 
\[
\begin{cases}
x^2 - y^2 - 10x + 16y - 64 = 0 \quad \text{(1)} \\
x^2 + y^2 - 10x - 16y + 64 = 0 \quad \text{(2)}
\end{cases}
\]

### c)
\[
\begin{cases}
2x^2 - 4y^2 = 8x \quad \text{(1)} \\
x^2 - 2y^2 - 4x = 0 \quad \text{(2)}
\end{cases}
\]

Would you like me to solve one of these systems for you? Let me know which one you'd like to start with, or if you'd like an explanation of how to apply either the substitution or elimination method.

Here are 5 related questions you might find helpful:
1. How does the elimination method work for nonlinear systems?
2. Can we always use substitution in nonlinear systems?
3. What happens when both equations contain quadratic terms?
4. How do we verify solutions for systems of nonlinear equations?
5. Are there graphical methods to solve these systems?

**Tip**: Always check if equations can be simplified before choosing a method. This can make the substitution or elimination easier.

Solve the following nonlinear systems of equations using either substitution or elimination method.

Learn how to solve systems of nonlinear equations, including quadratic terms, using the substitution or elimination method. Detailed problems with solutions suitable for students in higher grades.

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