The problem appears to involve determining the number of solutions for each system of linear equations by identifying if they have one solution, no solution, or infinitely many solutions.

Let's analyze each system given in the image:

1. System (1): y = 4x - 8$$ - Since the slopes of these two equations are different (5 and 4), the lines are not parallel, meaning they will intersect at exactly one point. - **Answer**: (a) One solution.
2. System (2): y = 8 + 2x$$ - Rearranging the second equation for consistency gives us the same equation as the first, $$y = 2x + 8$$. - Since these two equations are identical, they represent the same line, meaning every point on the line is a solution. - **Answer**: (c) Many solutions.
3. Graph (3):
   • The graph shows two lines that appear to be intersecting at one point.
   • This visual representation indicates that the two lines intersect at one unique point.
   • Answer: (a) One solution.

Would you like more details on how these solutions were determined or any other assistance with this topic?

Here are five related questions for further practice:

1. How can you determine if two lines are parallel or identical using their equations?
2. What are the steps to find the intersection point if there is one solution?
3. Can two lines have a unique solution if one is vertical and the other is horizontal? Why?
4. How can systems of linear equations be solved graphically?
5. What are the properties of a system of equations that has no solution?

Tip: To quickly determine the number of solutions in linear equations, compare the slopes and y-intercepts—different slopes indicate one solution, identical slopes with different intercepts indicate no solution, and identical lines indicate infinitely many solutions.