Which of the following points are solutions to the system of inequalities shown below?
Check all that apply.
x+y22+4 y < 4
A. (7,-1)
B. (5,3)
C. (1,-1)
D. (3,7)
E. (2,5)
F. (2,4

The system of inequalities seems to be written incorrectly. From your text, it appears that the intended inequality might be: 

\[
x + y < 4
\quad \text{and} \quad y < 4
\]

Assuming these are the two inequalities, let’s test each point to determine which ones satisfy both conditions.

---

### 1. System of inequalities:  
1. **\(x + y < 4\)**  
2. **\(y < 4\)**  

### Now, check the points:

**A. (7, -1)**  
1. \(7 + (-1) = 6\), which is **not** less than 4.  
This point **does not** satisfy the first inequality.  

**B. (5, 3)**  
1. \(5 + 3 = 8\), which is **not** less than 4.  
This point **does not** satisfy the first inequality.

**C. (1, -1)**  
1. \(1 + (-1) = 0\), which is less than 4. ✅  
2. \(-1 < 4\) ✅  
This point **satisfies both inequalities**.

**D. (3, 7)**  
1. \(3 + 7 = 10\), which is **not** less than 4.  
This point **does not** satisfy the first inequality.

**E. (2, 5)**  
1. \(2 + 5 = 7\), which is **not** less than 4.  
This point **does not** satisfy the first inequality.

**F. (2, 4)**  
1. \(2 + 4 = 6\), which is **not** less than 4.  
This point **does not** satisfy the first inequality.

---

### Solution:
Only **C. (1, -1)** satisfies both inequalities.

---

Would you like further details or clarification?  
Here are some related questions to explore next:

1. What is the geometric interpretation of inequalities on a graph?
2. How do you solve systems with both equations and inequalities?
3. What happens if both inequalities involve \( \leq \) or \( \geq \)?
4. How do we represent multiple solutions graphically for systems of inequalities?
5. Can inequalities have infinite solutions?

**Tip:** Always check each inequality separately to avoid missing valid solutions.

Which of the following points are solutions to the system of inequalities shown below? Check all that apply. x + y < 4 and y < 4 A. (7,-1) B. (5,3) C. (1,-1) D. (3,7) E. (2,5) F. (2,4)

Learn how to solve a system of inequalities involving x + y < 4 and y < 4 by testing multiple points to find valid solutions. This problem demonstrates key algebraic concepts and is suitable for students in Grades 7-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation