Which of the following graphs accurately represents the solution to the system of inequalities?

Graph showing two linear inequalities with shaded solution regions and a red arrow indicating a boundary line.

Graph showing shaded region representing the solution to a system of linear inequalities on an xy-coordinate plane.

Graph showing shaded regions representing solutions to a system of linear inequalities on an xy-coordinate plane.

Verified step by step guidance

Step 1: Identify the inequalities given: $y \geq 3x - 1$ and $y < 3$.

Step 2: For $y \geq 3x - 1$, graph the line $y = 3x - 1$ with a solid line because the inequality includes equality ($\geq$). Shade the region above this line since $y$ is greater than or equal to \$3x - 1$.

Step 3: For $y < 3$, graph the horizontal line $y = 3$ with a dashed line because the inequality is strict (<). Shade the region below this line since $y$ is less than 3.

Step 4: The solution to the system is the intersection of the shaded regions from both inequalities. This means the area above or on the line $y = 3x - 1$ and below the line $y = 3$.

Step 5: Compare the graphs provided to find the one where the shaded region lies above the solid line $y = 3x - 1$ and below the dashed line $y = 3$. The correct graph will show this overlapping shaded region.

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