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 points are solutions to the inequalities \(y > 3x + 1\) and \(y \leq 2x + 5\), you need to analyze both inequalities.

1. Inequality \(y > 3x + 1\): This represents a region above the line \(y = 3x + 1\).
2. Inequality \(y \leq 2x + 5\): This represents a region below or on the line \(y = 2x + 5\).

The area where both inequalities hold true is where \(y\) is above the line \(y = 3x + 1\) and below or on the line \(y = 2x + 5\).

Since I am not able to see an image, I cannot identify the specific points plotted on your graph. However, you can go through the following steps to find the correct point:

1. Test points: Choose each of the plotted points (with their \(x\) and \(y\) coordinates) and substitute them into both inequalities.

2. Substitution:

   • For a point \((x, y)\), verify if:
     • \(y > 3x + 1\)
     • \(y \leq 2x + 5\)

3. The selected point must satisfy both inequalities simultaneously.

Once you check these inequalities against each of the plotted points, the correct solution will be the point that satisfies both conditions.

If you have specific coordinates, please provide them, and I can help you verify which point is a solution to the inequalities!