A coordinate plane featuring the following: - A solid line passing through the ordered pairs, $$ (-1,5),(-1,0) $$, and $$ (-1,-5) $$ - A shaded region left of this line. - One solid line passing through the ordered pairs, $$ (3,5),(3,0) $$, and ( $$ 3,-5 $$ ). - A shaded region right of this line. The system does have an infinite number of solutions.

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Based on your description, you're outlining a coordinate plane with two vertical lines and their corresponding shaded regions. Let's break down the components and define the system of inequalities that represents this scenario.

### Components Described:

1. **First Vertical Line:**
   - Passes through the points $$ (-1, 5) $$, $$ (-1, 0) $$, and $$ (-1, -5) $$.
   - This is the line $$ x = -1 $$.
   - **Shaded Region:** To the **left** of this line, which includes all points where $$ x $$ is less than or equal to $$-1$$.

2. **Second Vertical Line:**
   - Passes through the points $$ (3, 5) $$, $$ (3, 0) $$, and $$ (3, -5) $$.
   - This is the line $$ x = 3 $$.
   - **Shaded Region:** To the **right** of this line, which includes all points where $$ x $$ is greater than or equal to $$3$$.

### System of Inequalities:

To represent the shaded regions described, we can set up the following inequalities:

1. **For the Left-Shaded Region:**
   $$
   x \leq -1
   $$
   
2. **For the Right-Shaded Region:**
   $$
   x \geq 3
   $$

### Combined System:

Since the shaded regions are to the left of $$ x = -1 $$ **or** to the right of $$ x = 3 $$, the system of inequalities can be expressed using an **OR** condition:

$$
\begin{cases}
x \leq -1 \
x \geq 3
\end{cases}
$$

### Solution Set:

- **Infinite Solutions:** The system has an infinite number of solutions because there are infinitely many points that satisfy either $$ x \leq -1 $$ or $$ x \geq 3 $$.
  
- **Graphical Representation:**
  - **Line $$ x = -1 $$:** All points on and to the left side (including the line) are solutions.
  - **Line $$ x = 3 $$:** All points on and to the right side (including the line) are solutions.

### Visual Summary:

```
Number Line Representation:

<----|=============|---->
    -1             3

Shaded regions:
- All points to the left of -1 (including -1)
- All points to the right of 3 (including 3)
```

### Conclusion:

The system you've described consists of two inequalities, $$ x \leq -1 $$ **or** $$ x \geq 3 $$, which together define two distinct regions on the coordinate plane. Since there are infinitely many points that satisfy either of these conditions, the system indeed has an infinite number of solutions.
The system consists of two inequalities: $$ x \leq -1 $$ or $$ x \geq 3 $$. This means all points to the left of -1 and all points to the right of 3 are solutions, resulting in an infinite number of solutions.

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