https://file.aiquickdraw.com/mathbot/file/1726702679175o4zq9heb.jpg

The system of equations provided in the image is:

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

### Step 1: Simplify the first equation

The first equation can be simplified by dividing the entire equation by \(-2\) to put it in slope-intercept form:
\[
-6x - 2y = 6 \quad \text{(Divide by -2)} \quad 3x + y = -3
\]
Thus, the first equation becomes:
\[
y = -3x - 3
\]

### Step 2: Compare both equations
The system now consists of:
1. \( y = -3x - 3 \)
2. \( y = -3x - 2 \)

These are two parallel lines since both have the same slope \(-3\), but different y-intercepts (\(-3\) and \(-2\)). 

### Step 3: Conclusion
Parallel lines never intersect, which means there is **no solution** to this system of equations.

Therefore, the correct solution is **"No solution."**

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Would you like more details, or do you have any questions?

Here are 5 related questions you might find interesting:
1. How do we determine if two lines are parallel by looking at their equations?
2. What is the significance of the slope and y-intercept in a linear equation?
3. How can we verify graphically that two lines do not intersect?
4. How does solving a system of equations change when using substitution versus graphing?
5. What does it mean when a system of equations has "infinitely many solutions"?

**Tip:** When two equations in a system have the same slope but different y-intercepts, the system will always have no solution because the lines are parallel.

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

Explore the graphing of the system of equations -6x - 2y = 6 and y = -3x - 2. Learn how to identify parallel lines and determine that the system has no solution by comparing the slopes and y-intercepts of the equations. This problem is suitable for students in Grades 8-10 studying algebra and graphing systems of equations.

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