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.

Question

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)
(
,
)
Remaining Attempts : 3

Answer 1

To determine which of the given points satisfies the inequalities \(y > 3x + 1\) and \(y \leq 2x + 5\), we can analyze each inequality separately.

1. Inequality 1: \(y > 3x + 1\)

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

2. Inequality 2: \(y \leq 2x + 5\)

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

To find the points that satisfy both inequalities, we need to check each point provided on the graph against these conditions.

Since the specific points are not listed in your question, I will give a general method for checking:

• For any point \( (x, y) \):
  • Check \( y > 3x + 1 \): Calculate \(3x + 1\) and see if \(y\) is greater.
  • Check \( y \leq 2x + 5 \): Calculate \(2x + 5\) and see if \(y\) is less than or equal to that.

After you test each point on the graph using these inequalities, you will find the point that satisfies both conditions. If you can provide the coordinates of the three points, I can help identify the correct point specifically.

Answer 2

The coordinates are -1,2 and -5,5 and 9,5

Answer 3

Let's evaluate each point to see if it satisfies the inequalities \( y > 3x + 1 \) and \( y \leq 2x + 5 \).

1. Point (-1, 2):

   • Check \( y > 3x + 1 \): \[ 2 > 3(-1) + 1 \implies 2 > -3 + 1 \implies 2 > -2 \quad \text{(True)} \]
   • Check \( y \leq 2x + 5 \): \[ 2 \leq 2(-1) + 5 \implies 2 \leq -2 + 5 \implies 2 \leq 3 \quad \text{(True)} \]

   Conclusion: (-1, 2) satisfies both inequalities.

2. Point (-5, 5):

   • Check \( y > 3x + 1 \): \[ 5 > 3(-5) + 1 \implies 5 > -15 + 1 \implies 5 > -14 \quad \text{(True)} \]
   • Check \( y \leq 2x + 5 \): \[ 5 \leq 2(-5) + 5 \implies 5 \leq -10 + 5 \implies 5 \leq -5 \quad \text{(False)} \]

   Conclusion: (-5, 5) does not satisfy both inequalities.

3. Point (9, 5):

   • Check \( y > 3x + 1 \): \[ 5 > 3(9) + 1 \implies 5 > 27 + 1 \implies 5 > 28 \quad \text{(False)} \]
   • Check \( y \leq 2x + 5 \): \[ 5 \leq 2(9) + 5 \implies 5 \leq 18 + 5 \implies 5 \leq 23 \quad \text{(True)} \]

   Conclusion: (9, 5) does not satisfy both inequalities.

Based on this evaluation, the point that satisfies both inequalities \( y > 3x + 1 \) and \( y \leq 2x + 5 \) is:

(-1, 2).