Kelley was asked to graph the following system of equations and estimate the solution on her graph. 2x+ 5y = 7 ×+ 4y= 2 Kelley's solution steps and graph are below. Did she solve the problem correctly? If applicable, identify the steps where any mistakes were made and provide the correct solution and graph.
Kelley was asked to graph the following system of equations and estimate the solution on her graph. 2x+ 5y = 7 ×+ 4y= 2 Kelley's solution steps and graph are below. Did she solve the problem correctly? If applicable, identify the steps where any mistakes were made and provide the correct solution and graph.
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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Question
Kelley was asked to graph the following system of equations and estimate the solution on her graph.
2x+ 5y = 7
×+ 4y= 2
Kelley's solution steps and graph are below. Did she solve the problem correctly? If applicable, identify the steps where any mistakes were made and provide the correct solution and graph.
Transcribed Image Text:### Algebraic Equations and Graphical Solutions
This section provides different algebraic equations and a graph to demonstrate their relationships.
#### Equations:
- **A**: \( 2x + 5y = 7 \)
- **B**: \( 5y = 2x + 7 \)
- **C**: \( y = \frac{2}{5}x + \frac{7}{5} \)
- **D**: \( x + 4y = 2 \)
- **E**: \( 4y = -x + 2 \)
- **F**: \( y = -\frac{1}{4}x + 2 \)
#### Graph Explanation:
Below these equations is a graph with two lines. The graph is a Cartesian coordinate system with:
- **X-axis** ranging from -5 to 10.
- **Y-axis** ranging from 0 to 6.
The lines:
1. **Line 1 (Purple)** starts with a negative slope, crossing the x-axis between 5 and 10, and the y-axis near 6.
2. **Line 2 (Blue)** starts with a positive slope, crossing the y-axis at 2 and the x-axis at 5.
The point of intersection is marked as \( (1, 2) \), which represents the solution to the system of equations represented by the lines.
This example demonstrates how systems of linear equations can be graphically solved by plotting the equations and observing the intersection points.
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