Find the solutions to the system of nonlinear equations given by: Sy= = - x - 12 x² + y² = 80 A: B: Use the graph to determine which point is A and B. Enter your answer as an ordered pair. For example: (2, - 5)
Find the solutions to the system of nonlinear equations given by: Sy= = - x - 12 x² + y² = 80 A: B: Use the graph to determine which point is A and B. Enter your answer as an ordered pair. For example: (2, - 5)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![**Title: Solving Systems of Nonlinear Equations**
**Problem Statement:**
Find the solutions to the system of nonlinear equations given by:
\[
\begin{cases}
y = -x - 12 \\
x^2 + y^2 = 80
\end{cases}
\]
**Graph Illustration:**
The graph illustrates a circle and a straight line. The equation \( x^2 + y^2 = 80 \) represents the circle. The equation \( y = -x - 12 \) represents the straight line. The points of intersection of the circle and the line are labeled as points A and B on the graph.
**Solution Steps:**
Use the graph to determine the coordinates of points A and B, where the line intersects the circle. Enter your answers in the text boxes provided.
**Answer Input:**
- A: [Enter your answer as an ordered pair. For example: (2, -5)]
- B: [Enter your answer as an ordered pair. For example: (2, -5)]
**Instructions:**
1. Observe the graph closely to identify the coordinates where the line intersects the circle.
2. Input the coordinates of points A and B into the respective text boxes.
3. Ensure your answers are in the format of an ordered pair, such as (x, y).
By solving this problem, you will understand how to find the points of intersection in a system of nonlinear equations graphically.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F53b99f33-5097-48ca-9202-113ad6b052b9%2F3cb26b5c-d418-45a3-9792-a563449e456c%2Fmlkbbyb_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Solving Systems of Nonlinear Equations**
**Problem Statement:**
Find the solutions to the system of nonlinear equations given by:
\[
\begin{cases}
y = -x - 12 \\
x^2 + y^2 = 80
\end{cases}
\]
**Graph Illustration:**
The graph illustrates a circle and a straight line. The equation \( x^2 + y^2 = 80 \) represents the circle. The equation \( y = -x - 12 \) represents the straight line. The points of intersection of the circle and the line are labeled as points A and B on the graph.
**Solution Steps:**
Use the graph to determine the coordinates of points A and B, where the line intersects the circle. Enter your answers in the text boxes provided.
**Answer Input:**
- A: [Enter your answer as an ordered pair. For example: (2, -5)]
- B: [Enter your answer as an ordered pair. For example: (2, -5)]
**Instructions:**
1. Observe the graph closely to identify the coordinates where the line intersects the circle.
2. Input the coordinates of points A and B into the respective text boxes.
3. Ensure your answers are in the format of an ordered pair, such as (x, y).
By solving this problem, you will understand how to find the points of intersection in a system of nonlinear equations graphically.
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