Question

The ordered pairs in the table are possible solutions to the given equations.

Match each ordered pair to the equation for which it is a solution. Ordered pairs may be used more than once.

Neither
(-5, 0)



(0, -5)



(0, 2)



(1, 6)

Answer 1

To determine which ordered pairs are solutions to which equations, we need the equations to match the forms of the possible solutions. However, as you didn't provide the specific equations, I'll assume some common forms of linear equations (e.g., \(y = mx + b\)) and show you how to evaluate each ordered pair against them.

Let's analyze hypothetical equations of the form:

1. **Equation 1:** \(y = 2x + 2\)
2. **Equation 2:** \(y = -x - 5\)
3. **Equation 3:** \(y = 3x + 3\)
4. **Equation 4:** \(y = 5 - x\)

Now let's evaluate the ordered pairs:

- **For (-5, 0):**
- **Equation 1:** \(0 = 2(-5) + 2 \to 0 = -10 + 2 \to 0 = -8\) (Not a solution)
- **Equation 2:** \(0 = -(-5) - 5 \to 0 = 5 - 5 \to 0 = 0\) (Solution)
- **Equation 3:** \(0 = 3(-5) + 3 \to 0 = -15 + 3 \to 0 = -12\) (Not a solution)
- **Equation 4:** \(0 = 5 - (-5) \to 0 = 5 + 5 \to 0 = 10\) (Not a solution)

- **For (0, -5):**
- **Equation 1:** \(-5 = 2(0) + 2 \to -5 = 0 + 2 \to -5 = 2\) (Not a solution)
- **Equation 2:** \(-5 = -(0) - 5 \to -5 = 0 - 5 \to -5 = -5\) (Solution)
- **Equation 3:** \(-5 = 3(0) + 3 \to -5 = 0 + 3 \to -5 = 3\) (Not a solution)
- **Equation 4:** \(-5 = 5 - (0) \to -5 = 5 - 0 \to -5 = 5\) (Not a solution)

- **For (0, 2):**
- **Equation 1:** \(2 = 2(0) + 2 \to 2 = 0 + 2 \to 2 = 2\) (Solution)
- **Equation 2:** \(2 = -(0) - 5 \to 2 = 0 - 5 \to 2 = -5\) (Not a solution)
- **Equation 3:** \(2 = 3(0) + 3 \to 2 = 0 + 3 \to 2 = 3\) (Not a solution)
- **Equation 4:** \(2 = 5 - (0) \to 2 = 5 - 0 \to 2 = 5\) (Not a solution)

- **For (1, 6):**
- **Equation 1:** \(6 = 2(1) + 2 \to 6 = 2 + 2 \to 6 = 4\) (Not a solution)
- **Equation 2:** \(6 = -(1) - 5 \to 6 = -1 - 5 \to 6 = -6\) (Not a solution)
- **Equation 3:** \(6 = 3(1) + 3 \to 6 = 3 + 3 \to 6 = 6\) (Solution)
- **Equation 4:** \(6 = 5 - (1) \to 6 = 5 - 1 \to 6 = 4\) (Not a solution)

To conclude your matching:

- **(-5, 0)** is a solution for **Equation 2**
- **(0, -5)** is a solution for **Equation 2**
- **(0, 2)** is a solution for **Equation 1**
- **(1, 6)** is a solution for **Equation 3**

If you have specific equations or need assistance with different types, please provide them for re-evaluation.