A linear system has an infinite number of solutions if the two equations represent the same line. This occurs when both equations simplify to the same linear equation.
In your options, the graph that shows the same line represented by both equations (meaning they overlap perfectly) will indicate that the system has an infinite number of solutions.
From your descriptions, the second option is the key point to note:
- The second graph features two parallel lines, which will not have any solutions since they never intersect.
- The fourth option features two intersecting lines, indicating a unique solution.
- However, the first option shows only one line which represents the equation \( y = -x + 6 \), and it does not indicate another line, which might suggest the infinite solutions if it’s a repeated representation.
For the infinite solutions, specifically check if there is an exact overlap (the same line drawn multiple times or as two lines perfectly on top of each other). None of the given options clearly mention such visualization.
Let’s clarify:
- If the first option is just showing one line through points (0,6) and (6,0), there are different interpretations. Repetitions of this line would mean infinite solutions and you would want something showing this identical line.
Please provide clarification on if you have exact pairs (like identities) being depicted in these graphs, as usually visual representation might be slightly off. The likely assumption leads to answer towards singular lines to interpret infinite solutions, so please align the definitions closely!