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The problem asks us to determine if a system of equations has infinitely many solutions, no solution, or a unique solution represented by an ordered pair. Additionally, we need to choose the statement that best explains why the chosen solution type is correct. Based on the image, option B "There are infinitely many solutions" is already selected. We need to select the correct reasoning.

AlgebraSystems of EquationsLinear EquationsSolution TypesGraphical Interpretation
2025/3/13

1. Problem Description

The problem asks us to determine if a system of equations has infinitely many solutions, no solution, or a unique solution represented by an ordered pair. Additionally, we need to choose the statement that best explains why the chosen solution type is correct. Based on the image, option B "There are infinitely many solutions" is already selected. We need to select the correct reasoning.

2. Solution Steps

When a system of equations has infinitely many solutions, it means that the two equations are essentially the same line. Graphically, this means that the two lines coincide. If the graphs intersect at one point, the solution is unique. If the graphs never intersect, there is no solution.
Therefore, the correct statement is "The graphs of the two equations represent the same line."

3. Final Answer

There are infinitely many solutions.
The graphs of the two equations represent the same line.

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