dentify the ordered pair that satisfies both equations.

y=2x+15 	(-4,7),(7,-4),(-7,1)

y=-2x-1

We need to identify which of the ordered pairs \((-4, 7)\), \((7, -4)\), and \((-7, 1)\) satisfies both equations:

1. \( y = 2x + 15 \)
2. \( y = -2x - 1 \)

To solve this, we will substitute each ordered pair into **both** equations and check if it satisfies them.

### 1. For the pair \((-4, 7)\):
- **Substitute into the first equation** \(y = 2x + 15\):
  \[
  7 = 2(-4) + 15
  \]
  Simplifying:
  \[
  7 = -8 + 15 = 7
  \]
  This satisfies the first equation.

- **Substitute into the second equation** \(y = -2x - 1\):
  \[
  7 = -2(-4) - 1
  \]
  Simplifying:
  \[
  7 = 8 - 1 = 7
  \]
  This satisfies the second equation as well.

Thus, \((-4, 7)\) satisfies both equations.

### 2. For the pair \((7, -4)\):
- **Substitute into the first equation** \(y = 2x + 15\):
  \[
  -4 = 2(7) + 15
  \]
  Simplifying:
  \[
  -4 = 14 + 15 = 29
  \]
  This **does not** satisfy the first equation.

Since the first equation is not satisfied, we can skip checking the second equation for this pair.

### 3. For the pair \((-7, 1)\):
- **Substitute into the first equation** \(y = 2x + 15\):
  \[
  1 = 2(-7) + 15
  \]
  Simplifying:
  \[
  1 = -14 + 15 = 1
  \]
  This satisfies the first equation.

- **Substitute into the second equation** \(y = -2x - 1\):
  \[
  1 = -2(-7) - 1
  \]
  Simplifying:
  \[
  1 = 14 - 1 = 13
  \]
  This **does not** satisfy the second equation.

### Conclusion:
The ordered pair \((-4, 7)\) satisfies **both** equations.

Would you like more details or further explanations?

Here are 5 related questions for further exploration:
1. How do we graph the two equations to visualize their intersection?
2. Can you find other points where the two equations might intersect?
3. What is the process for solving a system of linear equations algebraically?
4. How do you solve a system of equations using substitution or elimination?
5. What happens if the lines represented by these equations are parallel?

**Tip:** For solving systems of linear equations, always check both equations with the given points. Graphing the lines can also provide a visual confirmation.

Identify the ordered pair that satisfies both equations.
y=2x+15 (-4,7),(7,-4),(-7,1)
y=-2x-1

Learn how to identify which ordered pair satisfies both linear equations y = 2x + 15 and y = -2x - 1. This step-by-step solution explains how to substitute each pair into the equations and verify the results. Suitable for Grades 8-10 students studying systems of linear equations.

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