Question

x+2y≥103x−4y>12Which of the following ordered pairs are solutions to the system? Select all that apply.(2 points)Responses(4,−4)open paren 4 comma negative 4 close paren(10,2)open paren 10 comma 2 close paren(14,−1)open paren 14 comma negative 1 close paren(−4,2)open paren negative 4 comma 2 close paren(2,6)open paren 2 comma 6 close paren(8,1)open paren 8 comma 1 close paren(16,

Answer 1

To determine which ordered pairs are solutions to the given system of inequalities, we need to plug each pair into both inequalities:

1. \( x + 2y \geq 10 \)
2. \( 3x - 4y > 12 \)

We will check each possible ordered pair:

1. **(4, -4)**:
- For the first inequality: \( 4 + 2(-4) = 4 - 8 = -4 \) (not ≥ 10)
- For the second inequality: \( 3(4) - 4(-4) = 12 + 16 = 28 \) (> 12)
- **Not a solution**.

2. **(10, 2)**:
- For the first inequality: \( 10 + 2(2) = 10 + 4 = 14 \) (≥ 10)
- For the second inequality: \( 3(10) - 4(2) = 30 - 8 = 22 \) (> 12)
- **Solution**.

3. **(14, -1)**:
- For the first inequality: \( 14 + 2(-1) = 14 - 2 = 12 \) (not ≥ 10)
- For the second inequality: \( 3(14) - 4(-1) = 42 + 4 = 46 \) (> 12)
- **Not a solution**.

4. **(-4, 2)**:
- For the first inequality: \( -4 + 2(2) = -4 + 4 = 0 \) (not ≥ 10)
- For the second inequality: \( 3(-4) - 4(2) = -12 - 8 = -20 \) (not > 12)
- **Not a solution**.

5. **(2, 6)**:
- For the first inequality: \( 2 + 2(6) = 2 + 12 = 14 \) (≥ 10)
- For the second inequality: \( 3(2) - 4(6) = 6 - 24 = -18 \) (not > 12)
- **Not a solution**.

6. **(8, 1)**:
- For the first inequality: \( 8 + 2(1) = 8 + 2 = 10 \) (≥ 10)
- For the second inequality: \( 3(8) - 4(1) = 24 - 4 = 20 \) (> 12)
- **Solution**.

**Summary of solutions**:
- **(10, 2)**
- **(8, 1)**

Therefore, the solutions to the system of inequalities are **(10, 2)** and **(8, 1)**.