To determine which graph shows that the system of equations \(3x + 2y = 12\) and \(6x + 4y = 24\) has an infinite number of solutions, we can first recognize that these two equations are actually equivalent. The second equation can be derived by multiplying the first equation by 2. This means both equations represent the same line, which indicates that there are infinitely many solutions (all the points on the line).
Given this, the correct graph will show the same line plotted twice, which signifies that there is no alternative point of intersection, confirming the infinite solutions.
Among the options:
- A single line – Indicates one unique solution (not the answer).
- Two intersecting lines – Indicates a unique solution (not the answer).
- Two parallel lines – Indicates no solution (not the answer).
- A single line – Indicates one unique solution (not the answer).
The graph that indicates both equations are the same would show two identical lines on top of each other representing infinite solutions, but none of the described options showcase this clearly.
If an option showed two overlapping lines (which is not explicitly described herein), that would indicate an infinite number of solutions. Since none of the graphs presented explicitly indicate overlapping lines, the accurate representation would typically involve visual overlap, which seems not to be in the choices.
However, the graph with two parallel lines is a clear indicator of a setup that does not yield a solution, confirming that the other options do not encapsulate the infinite solutions scenario by virtue of no overlap representation.
I'll clarify that the correct answer should ideally show two identical lines for infinite solutions, but since that option does not exist among the choices, I would advise focusing on the other factors or confirming the potential overlap had to been represented in your visual choices appropriately. The apparent solution doesn't align closely with the problem as described.
Based on traditional expectations, if accessing is possible, the idea of confirming which option; seeing the two lines depicted in a manner that they do trace over one another is essential. In absence of that direct choice, your interpretation might lean towards careful reevaluation of representation symbols from existing examples.