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The task asks to find linear systems of equations for three different graphs (a, b, and c), and to determine the solution sets for each system.

### Step-by-step Approach:

1. **Graph (a)**:
    - There are two lines, which intersect at the point \((-1, 2)\). 
    - First line: Slope is negative, passing through points like \((0, 1)\) and \((1, 0)\). This gives the equation of the form \( y = -x + 1 \).
    - Second line: Slope is positive, passing through points like \((0, -2)\) and \((1, 0)\), resulting in \( y = 2x - 2 \).
    - The system is:
      \[
      \begin{cases}
      y = -x + 1 \\
      y = 2x - 2
      \end{cases}
      \]
    - The solution is \((-1, 2)\), where the two lines intersect.

2. **Graph (b)**:
    - The lines appear to be parallel, meaning they do not intersect (no solution).
    - First line: The slope is negative, passing through \((0, 4)\) and \((1, 3)\), giving the equation \( y = -x + 4 \).
    - Second line: Also has a negative slope, passing through \((0, 2)\) and \((1, 1)\), which results in \( y = -x + 2 \).
    - The system is:
      \[
      \begin{cases}
      y = -x + 4 \\
      y = -x + 2
      \end{cases}
      \]
    - Since the lines are parallel, there is **no solution**.

3. **Graph (c)**:
    - The lines coincide, meaning every point on one line is also on the other (infinite solutions).
    - First line: Slope is positive, passing through \((0, 2)\) and \((2, 4)\), giving the equation \( y = x + 2 \).
    - Second line: It is the same line as the first one, so the equation is also \( y = x + 2 \).
    - The system is:
      \[
      \begin{cases}
      y = x + 2 \\
      y = x + 2
      \end{cases}
      \]
    - The solution is **infinite** as the lines are identical.

### Summary of Solution Sets:
- a) The solution is \((-1, 2)\).
- b) There is no solution.
- c) There are infinitely many solutions.

Would you like further explanation on any of these graphs or concepts?

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### Related Questions:
1. How do you find the slope of a line from a graph?
2. How can you determine if two lines are parallel by just looking at their equations?
3. What does it mean when a system of equations has no solution?
4. How do we algebraically solve a system of linear equations with two variables?
5. What is the geometric meaning of an infinite number of solutions?

### Tip:
Parallel lines have the same slope but different y-intercepts, which is why they never intersect.

Solve a system of linear equations that corresponds to the given graph and provide the solution set.

This problem involves solving systems of linear equations by graphing. It covers key algebraic concepts such as slope-intercept form, parallel lines, and coinciding lines. Learn how to analyze the intersection of lines to find the solution set.

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