It seems you have provided an inequality: \( x + y \geq 2 \).

To analyze this inequality, we can follow these steps:

1. **Identify the inequality**: The inequality states that the sum of \( x \) and \( y \) must be greater than or equal to 2.

2. **Graphical representation**: This inequality can be represented graphically on a coordinate plane. The line \( x + y = 2 \) serves as the boundary. The area above this line (including the line itself) represents the solutions to the inequality.

3. **Finding intercepts**:
   - To find the x-intercept, set \( y = 0 \):
     \[
     x + 0 = 2 \implies x = 2
     \]
   - To find the y-intercept, set \( x = 0 \):
     \[
     0 + y = 2 \implies y = 2
     \]
   - Thus, the intercepts are \( (2, 0) \) and \( (0, 2) \).

4. **Shading the region**: Since the inequality is \( \geq \), we will shade the region above the line \( x + y = 2 \), including the line itself.

If you need further analysis or specific solutions for values of \( x \) and \( y \) that satisfy this inequality, please let me know!

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Question

1. \( x+y \geq 2 \)

Ask by Chavez Howell. in the United States

Jan 23,2025

Real Tutor Solution

Tutor-Verified Answer

Answer

The inequality \( x + y \geq 2 \) means that the sum of \( x \) and \( y \) must be at least 2. This can be represented on a graph with the line \( x + y = 2 \) as the boundary. The solutions lie above this line, including the line itself.

Solution

It seems you have provided an inequality: \( x + y \geq 2 \). To analyze this inequality, we can follow these steps: 1. **Identify the inequality**: The inequality states that the sum of \( x \) and \( y \) must be greater than or equal to 2. 2. **Graphical representation**: This inequality can be represented graphically on a coordinate plane. The line \( x + y = 2 \) serves as the boundary. The area above this line (including the line itself) represents the solutions to the inequality. 3. **Finding intercepts**: - To find the x-intercept, set \( y = 0 \): \[ x + 0 = 2 \implies x = 2 \] - To find the y-intercept, set \( x = 0 \): \[ 0 + y = 2 \implies y = 2 \] - Thus, the intercepts are \( (2, 0) \) and \( (0, 2) \). 4. **Shading the region**: Since the inequality is \( \geq \), we will shade the region above the line \( x + y = 2 \), including the line itself. If you need further analysis or specific solutions for values of \( x \) and \( y \) that satisfy this inequality, please let me know!

Reviewed and approved by the UpStudy tutoring team

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Mind Expander

Did you know that this inequality represents a region in a two-dimensional space? Specifically, it describes the area above and including the line \(x + y = 2\). Not only does this line have a positive slope, but any point (x, y) that satisfies this inequality must also lie in the first quadrant if both x and y are non-negative. This makes it a fundamental concept in linear programming, where we often need to maximize or minimize certain functions over defined regions! When solving inequalities like this, a common mistake is to overlook the need to express the solution set properly. It's essential to remember that when you graph inequalities, you must shade the entire solution region. Moreover, if there are multiple inequalities, be sure to find the intersection of their regions, as that will give you the feasible zone for solutions!

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