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2. 4x-2y = -8 %3D 4x y = 2x + 4 %3D 241 -2

2. 4x-2y = -8 %3D 4x y = 2x + 4 %3D 241 -2

Advanced Engineering Mathematics
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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Certainly! Below is a transcription of the image suited for an educational website: --- **Lesson: Solving Systems of Equations by Graphing** **Example 2:** *Equations:* 1. \( 4x - 2y = -8 \) 2. \( y = 2x + 4 \) *Graph Description:* The provided graph is a standard coordinate plane with x-axis and y-axis ranging from -6 to 6. Each axis is marked at intervals of 1 unit. This graph will be used to plot the given equations to find their point of intersection, which represents the solution to the system of equations. *Solution Steps:* 1. **Rearrange Equation 1 into Slope-Intercept Form (y = mx + b):** - Start with \( 4x - 2y = -8 \) - Subtract \( 4x \) from both sides: \(-2y = -4x - 8\) - Divide by -2: \( y = 2x + 4 \) *Note:* In this case, both equations can be rewritten as \( y = 2x + 4 \), indicating that they might be the same line, and thus, there may be infinitely many solutions as they overlap completely. 2. **Graph the Equations:** - Plot the equation \( y = 2x + 4 \) on the graph. - Since both equations are identical, ensure the line represents both \( 4x - 2y = -8 \) and \( y = 2x + 4 \). *Observation:* If the lines overlap completely, the system of equations has infinitely many solutions, represented by all the points on the line \( y = 2x + 4 \). *Conclusion:* By graphing, you can visually identify the type of solution to the system of equations. Here, because the two equations are the same, it is clear that they represent the same line, hence infinitely many solutions exist. ---
Transcribed Image Text:Certainly! Below is a transcription of the image suited for an educational website: --- **Lesson: Solving Systems of Equations by Graphing** **Example 2:** *Equations:* 1. \( 4x - 2y = -8 \) 2. \( y = 2x + 4 \) *Graph Description:* The provided graph is a standard coordinate plane with x-axis and y-axis ranging from -6 to 6. Each axis is marked at intervals of 1 unit. This graph will be used to plot the given equations to find their point of intersection, which represents the solution to the system of equations. *Solution Steps:* 1. **Rearrange Equation 1 into Slope-Intercept Form (y = mx + b):** - Start with \( 4x - 2y = -8 \) - Subtract \( 4x \) from both sides: \(-2y = -4x - 8\) - Divide by -2: \( y = 2x + 4 \) *Note:* In this case, both equations can be rewritten as \( y = 2x + 4 \), indicating that they might be the same line, and thus, there may be infinitely many solutions as they overlap completely. 2. **Graph the Equations:** - Plot the equation \( y = 2x + 4 \) on the graph. - Since both equations are identical, ensure the line represents both \( 4x - 2y = -8 \) and \( y = 2x + 4 \). *Observation:* If the lines overlap completely, the system of equations has infinitely many solutions, represented by all the points on the line \( y = 2x + 4 \). *Conclusion:* By graphing, you can visually identify the type of solution to the system of equations. Here, because the two equations are the same, it is clear that they represent the same line, hence infinitely many solutions exist. ---
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