Solve the system of equations below both GRAPHICALLY and ANALYT- ICALLY. If the system has no solutions, say that it is inconsistent. 3x - 6y = 2 5x + 4y = 1
Solve the system of equations below both GRAPHICALLY and ANALYT- ICALLY. If the system has no solutions, say that it is inconsistent. 3x - 6y = 2 5x + 4y = 1
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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![**Problem 5: System of Equations**
**Objective:**
Solve the system of equations below both graphically and analytically. If the system has no solutions, declare it inconsistent.
**System of Equations:**
\[
\begin{cases}
3x - 6y = 2 \\
5x + 4y = 1
\end{cases}
\]
**Instructions:**
1. **Graphical Method**:
- Plot both equations on a coordinate plane to find the point of intersection, which represents the solution to the system.
- If the lines intersect at a single point, that point is the solution.
- If the lines are parallel and do not intersect, the system is inconsistent.
2. **Analytical Method**:
- Solve the equations algebraically using methods such as substitution or elimination to find the point where the two equations are equal.
- If you find a solution set, provide coordinates (x, y).
- If the system has no solution, state that it is inconsistent.
**Notes:**
- Ensure your graph is neatly labeled with a clear indication of the scale and where the two lines intersect or if they are parallel.
- Show all steps clearly for the analytical solution, explaining each part of the process.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18f586f2-2b12-4e9f-883a-779f80afdbe3%2F6c08daeb-a115-454e-9c20-ba88b71c8702%2Ftpffun_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Problem 5: System of Equations**
**Objective:**
Solve the system of equations below both graphically and analytically. If the system has no solutions, declare it inconsistent.
**System of Equations:**
\[
\begin{cases}
3x - 6y = 2 \\
5x + 4y = 1
\end{cases}
\]
**Instructions:**
1. **Graphical Method**:
- Plot both equations on a coordinate plane to find the point of intersection, which represents the solution to the system.
- If the lines intersect at a single point, that point is the solution.
- If the lines are parallel and do not intersect, the system is inconsistent.
2. **Analytical Method**:
- Solve the equations algebraically using methods such as substitution or elimination to find the point where the two equations are equal.
- If you find a solution set, provide coordinates (x, y).
- If the system has no solution, state that it is inconsistent.
**Notes:**
- Ensure your graph is neatly labeled with a clear indication of the scale and where the two lines intersect or if they are parallel.
- Show all steps clearly for the analytical solution, explaining each part of the process.
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