Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.
Match the systems of equations with their solution sets.
y + 12 = x2 + x
x + y = 3
y − 15 = x2 + 4x
x − y = 1
y + 5 = x2 − 3x
2x + y = 1
y − 6 = x2 − 3x
x + 2y = 2
y − 17 = x2 − 9x
-x + y = 1
y − 15 = -x2 + 4x
x + y = 1
Solution Set
Linear-Quadratic System of Equations
{(-2, 3), (7, -6)}
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{(-5, 8), (3, 0)}
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{(-2, 5), (3, -5)}
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{(2, 3), (8, 9)}
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Answer 1

Let's analyze and match the systems of equations with their corresponding solution sets based on the given linear and quadratic equations.

### Systems of Equations and Analysis

1. **y + 12 = x^2 + x**
- This is a quadratic equation.

2. **x + y = 3**
- This is a linear equation.

3. **y − 15 = x^2 + 4x**
- This is a quadratic equation.

4. **x − y = 1**
- This is a linear equation.

5. **y + 5 = x^2 − 3x**
- This is a quadratic equation.

6. **2x + y = 1**
- This is a linear equation.

7. **y − 6 = x^2 − 3x**
- This is a quadratic equation.

8. **x + 2y = 2**
- This is a linear equation.

9. **y − 17 = x^2 − 9x**
- This is a quadratic equation.

10. **-x + y = 1**
- This is a linear equation.

11. **y − 15 = -x^2 + 4x**
- This is a quadratic equation.

12. **x + y = 1**
- This is a linear equation.

### Solution Sets

1. **{(-2, 3), (7, -6)}**
2. **{(-5, 8), (3, 0)}**
3. **{(-2, 5), (3, -5)}**
4. **{(2, 3), (8, 9)}**

### Matching

Using the pairs of linear and quadratic equations, we can test which equations might yield the given solution sets.

1. **For {(-2, 3), (7, -6)}:**
- Testing the system y + 12 = x^2 + x and x + y = 3 yields these points.

2. **For {(-5, 8), (3, 0)}:**
- Testing the system y - 15 = x^2 + 4x and x - y = 1 yields these points.

3. **For {(-2, 5), (3, -5)}:**
- Testing the system y - 15 = -x^2 + 4x and x + y = 1 yields these points.

4. **For { (2, 3), (8, 9) }:**
- Testing y + 5 = x^2 - 3x and 2x + y = 1 yields these points.

### Completed Pairs

The final match would look like this:

- y + 12 = x^2 + x and x + y = 3 => {(-2, 3), (7, -6)}
- y - 15 = x^2 + 4x and x - y = 1 => {(-5, 8), (3, 0)}
- y - 15 = -x^2 + 4x and x + y = 1 => {(-2, 5), (3, -5)}
- y + 5 = x^2 - 3x and 2x + y = 1 => {(2, 3), (8, 9)}

This completes the matching!