https://file.aiquickdraw.com/mathbot/file/17267022869254f8orpoc.jpg

The system of equations provided in the image is:

\[
\begin{cases} 
-6x + 2y = -2 \\
y = 3x - 1
\end{cases}
\]

### Steps to solve this system graphically:

1. **Graph the second equation \( y = 3x - 1 \):**
   - This is already in slope-intercept form \( y = mx + b \), where \( m = 3 \) (slope) and \( b = -1 \) (y-intercept).
   - Plot the point \( (0, -1) \), then use the slope \( 3 \) (rise over run) to plot another point: move 3 units up and 1 unit to the right from \( (0, -1) \).

2. **Rearrange the first equation \( -6x + 2y = -2 \):**
   - Solve for \( y \):
   \[
   2y = 6x - 2
   \]
   \[
   y = 3x - 1
   \]
   - This equation is the same as the second equation \( y = 3x - 1 \), which means both equations represent the same line.

### Conclusion:
Since both equations represent the same line, the system has **infinitely many solutions**, meaning that every point on the line is a solution to the system.

The correct answer is **"infinitely many solutions."**

Would you like more details or have any further questions?

### Related Questions:
1. How can you identify a system with infinitely many solutions algebraically?
2. What happens when two lines are parallel but have different intercepts?
3. What is the graphical interpretation of a system with no solution?
4. How would you solve this system using substitution instead of graphing?
5. What does it mean if two lines intersect at one point in terms of solutions?

#### Tip: 
When two equations simplify to the same line, it always means the system has infinitely many solutions.

Graph the system of equations: -6x + 2y = -2 and y = 3x - 1, and write its solution.

This system of equations, -6x + 2y = -2 and y = 3x - 1, represents two identical lines when graphed. The solution involves graphing both lines and concluding that the system has infinitely many solutions because the two equations represent the same line.

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