Use the image to answer the question.

Question

A solid line, a dashed line, and three points are graphed on a coordinate plane. The x-axis ranges from negative 7 to 10 in increments of 1. The y-axis ranges from negative 5 to 7 in increments of 1.

Which of the points shown on the graph is a solution to the simultaneous inequalities y>3x+1 and y≤2x+5 ? Write the x-value first and the y-value second.

(1 point)
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Answer 1

To determine which of the points shown on the graph is a solution to the simultaneous inequalities \(y > 3x + 1\) and \(y \leq 2x + 5\), we would need to follow these steps:

1. Analyze the inequalities:

   • The first inequality \(y > 3x + 1\) represents the region above the line \(y = 3x + 1\).
   • The second inequality \(y \leq 2x + 5\) represents the region below or on the line \(y = 2x + 5\).

2. Find the intersection of the regions:

   • Both conditions must be satisfied simultaneously, meaning we need to check which points fall inside the area defined by these two inequalities.

3. Evaluate each point:

   • Without the actual graph or specific points provided, I cannot directly evaluate which point satisfies both inequalities.
   • Typically, you would substitute the coordinates of each point into both inequalities to verify whether they meet the criteria.

If you could provide the coordinates of the three points on the graph, I can determine which specific point is a solution to the inequalities.