To determine which graph shows that the linear system has an infinite number of solutions for the equations \(3x + 2y = 12\) and \(6x + 4y = 24\), we need to analyze the equations.
First, notice that the second equation can be rewritten as:
\[ 6x + 4y = 24 \implies \frac{6x}{2} + \frac{4y}{2} = \frac{24}{2} \implies 3x + 2y = 12 \]
This shows that the second equation is simply a scalar multiple (specifically, 2 times) of the first equation. Because both equations represent the same line, they will overlap completely.
A system of linear equations has an infinite number of solutions when the two equations represent the same line (i.e., they are dependent). Therefore, you are looking for a graph that shows a single line, and not two distinct lines intersecting at a point or parallel lines.
To summarize, look for a graph where both equations coincide, showing a single line rather than two lines. That graph will represent the linear system that has an infinite number of solutions.