To determine which graph shows that the system of linear equations \(3x + 2y = 12\) and \(6x + 4y = 24\) has an infinite number of solutions, we need to analyze the equations.
The second equation \(6x + 4y = 24\) can be simplified by dividing everything by 2, which yields:
\[ 3x + 2y = 12 \]
This means that both equations actually represent the same line. Therefore, they are equivalent and have infinitely many solutions since they overlap entirely.
Given this understanding, the graph that represents the same line for both equations is the one with two identical lines (i.e., one solid and one dotted) that coincide with each other.
Let's assess the options:
- The first option shows two intersecting lines, which means a unique solution.
- The second option shows a single line, which represents one equation.
- The third option shows two parallel lines, which indicates no solution.
- The fourth option shows one line, also representing one equation.
Based on this analysis, none of the descriptions provided perfectly match the representation of coinciding lines indicating an infinite number of solutions. If you are forced to choose among these, the closest possible representation for infinite solutions might typically appear as two overlapping lines, but if the scenarios don’t perfectly fit, there may be an error in the available options.
In conclusion, if the goal is to identify equivalent representations, the first option would indicate a misconception since they intersect. However, based on the context of depicting the scenario correctly, it can be confirmed that there should be selections that show lines coinciding, which are not found in the given options.