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)
(
,////

???
)

Answer 1

To determine which of the points is a solution to the simultaneous inequalities \( y > 3x + 1 \) and \( y \leq 2x + 5 \), we can analyze the inequalities.

1. For the first inequality \( y > 3x + 1 \):

   • This represents the area above the line \( y = 3x + 1 \).

2. For the second inequality \( y \leq 2x + 5 \):

   • This represents the area below or on the line \( y = 2x + 5 \).

Now, we need to find a point that lies in the region where \( y > 3x + 1 \) is true and \( y \leq 2x + 5 \) is also true.

Without the visual representation (the graph), I can’t determine the exact points plotted. However, here’s how you can find the answer:

1. Identify the equations of both lines:
   • \( y = 3x + 1 \) will be steeper than \( y = 2x + 5 \).
2. Mark the regions:
   • The area above the line \( y = 3x + 1 \) is where \( y > 3x + 1 \).
   • The area on or below the line \( y = 2x + 5 \) is where \( y \leq 2x + 5 \).
3. The solution(s) must lie in the intersection of these two shaded areas.

If you can provide the coordinates of the points shown in the graph, I can help you to identify which of those is the solution based on the given inequalities.