You and your friend are shopping at the the nearby Target store. You spent 78 dollars on 3 pounds of apples and 2 pounds of bananas. Your friend spent 200 dollars on 8 pounds of apples and 5 pounds of bananas. How much does apples and bananas cost per pound? (a) Let ₁ represent price of apples per pound and represent price of bananas per pound. Set up the equation for this problem as Ax=b, where (b) Solve manually (Please show your steps). X = [x1 x2
You and your friend are shopping at the the nearby Target store. You spent 78 dollars on 3 pounds of apples and 2 pounds of bananas. Your friend spent 200 dollars on 8 pounds of apples and 5 pounds of bananas. How much does apples and bananas cost per pound? (a) Let ₁ represent price of apples per pound and represent price of bananas per pound. Set up the equation for this problem as Ax=b, where (b) Solve manually (Please show your steps). X = [x1 x2
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Linear equation help, PLS more detals and clearly to see. If you don't know python, you can ignore the part C
![Below is the transcription of the given code snippet, which is intended for educational purposes on solving a system of linear equations using Python's `numpy` library.
---
**Educational Code Example: Solving Linear Equations**
In the code cell provided, we are tasked with completing the code required for part C. The code uses the `numpy` library to solve a system of linear equations.
```python
import numpy as np
A = ...
b = ...
x = np.linalg.solve(..., ...)
print("x1 is", x[0], "and x2 is", x[1])
```
**Explanation:**
- **import numpy as np**: This line imports the `numpy` library, which provides support for large, multi-dimensional arrays and matrices, along with mathematical functions to operate on these arrays.
- **A = ...** and **b = ...**: Here, `A` represents the coefficient matrix, and `b` represents the constant matrix (or vector). You need to replace `...` with the specific values or arrays.
- **x = np.linalg.solve(..., ...)**: This function is used to find the solution `x` to the linear equation system `Ax = b`. You must fill in the missing arguments with your defined matrices `A` and `b`.
- **print("x1 is", x[0], "and x2 is", x[1])**: This statement prints the solutions `x1` and `x2`, which correspond to the elements of solution vector `x`.
Use this template to understand how to solve linear systems efficiently using Python.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa98117fc-4537-4efb-9016-9993926a8208%2F0f327f7a-1683-4a95-8309-7efa10d646d4%2F4w8d60o_processed.png&w=3840&q=75)
Transcribed Image Text:Below is the transcription of the given code snippet, which is intended for educational purposes on solving a system of linear equations using Python's `numpy` library.
---
**Educational Code Example: Solving Linear Equations**
In the code cell provided, we are tasked with completing the code required for part C. The code uses the `numpy` library to solve a system of linear equations.
```python
import numpy as np
A = ...
b = ...
x = np.linalg.solve(..., ...)
print("x1 is", x[0], "and x2 is", x[1])
```
**Explanation:**
- **import numpy as np**: This line imports the `numpy` library, which provides support for large, multi-dimensional arrays and matrices, along with mathematical functions to operate on these arrays.
- **A = ...** and **b = ...**: Here, `A` represents the coefficient matrix, and `b` represents the constant matrix (or vector). You need to replace `...` with the specific values or arrays.
- **x = np.linalg.solve(..., ...)**: This function is used to find the solution `x` to the linear equation system `Ax = b`. You must fill in the missing arguments with your defined matrices `A` and `b`.
- **print("x1 is", x[0], "and x2 is", x[1])**: This statement prints the solutions `x1` and `x2`, which correspond to the elements of solution vector `x`.
Use this template to understand how to solve linear systems efficiently using Python.
![Title: Solving a System of Linear Equations to Determine Price per Pound
**Problem Statement:**
You and your friend are shopping at the nearby Target store. You spent \$78 on 3 pounds of apples and 2 pounds of bananas. Your friend spent \$200 on 8 pounds of apples and 5 pounds of bananas. How much do apples and bananas cost per pound?
**Tasks:**
(a) **Equation Setup:**
Define \( x_1 \) as the price of apples per pound and \( x_2 \) as the price of bananas per pound. Set up the equation for this problem in the form \( Ax = b \), where
\[
x = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
\]
(b) **Manual Solution:**
Solve the system of equations manually, showing each step.
(c) **Verification Using Python:**
Use Python to verify your result by employing `numpy.linalg.solve`. Fill in the blanks in the code provided.
Note: Ensure you document each step of the process, including setting up matrices and using computational tools to verify your solution.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa98117fc-4537-4efb-9016-9993926a8208%2F0f327f7a-1683-4a95-8309-7efa10d646d4%2Fbh9zv59_processed.png&w=3840&q=75)
Transcribed Image Text:Title: Solving a System of Linear Equations to Determine Price per Pound
**Problem Statement:**
You and your friend are shopping at the nearby Target store. You spent \$78 on 3 pounds of apples and 2 pounds of bananas. Your friend spent \$200 on 8 pounds of apples and 5 pounds of bananas. How much do apples and bananas cost per pound?
**Tasks:**
(a) **Equation Setup:**
Define \( x_1 \) as the price of apples per pound and \( x_2 \) as the price of bananas per pound. Set up the equation for this problem in the form \( Ax = b \), where
\[
x = \begin{bmatrix} x_1 \\ x_2 \end{bmatrix}
\]
(b) **Manual Solution:**
Solve the system of equations manually, showing each step.
(c) **Verification Using Python:**
Use Python to verify your result by employing `numpy.linalg.solve`. Fill in the blanks in the code provided.
Note: Ensure you document each step of the process, including setting up matrices and using computational tools to verify your solution.
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