Solve the system of equations by any method. 6x + 11y = 15 x + 2y = 4 Enter the exact answer as an ordered pair, (x, y).
Solve the system of equations by any method. 6x + 11y = 15 x + 2y = 4 Enter the exact answer as an ordered pair, (x, y).
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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![### Solving Systems of Equations
**Problem Statement:**
Solve the system of equations by any method.
\[
\begin{aligned}
6x + 11y &= 15 \\
x + 2y &= 4
\end{aligned}
\]
Enter the exact answer as an ordered pair, \((x, y)\).
If there is no solution, enter NS. If there is an infinite number of solutions, enter the general solution as an ordered pair in terms of \(x\).
---
### Explanation:
- **System of Equations:** A set of two or more equations that have common variables. Solving a system of equations means finding the values of the variables that satisfy all equations simultaneously.
- **Methods to Solve the System:**
- **Substitution Method:** Solve one of the equations for one variable and substitute this expression into the other equation.
- **Elimination Method:** Manipulate the equations to eliminate one variable, making it possible to solve for the remaining variable.
- **Graphical Method:** Graph the equations on a coordinate plane to find the point(s) of intersection.
- **Possible Outcomes:**
- A single solution \((x, y)\): The lines intersect at one point.
- No solution (NS): The lines are parallel and do not intersect.
- Infinite solutions: The lines coincide, meaning every point on one line is also on the other line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F314b57e5-7f54-41b9-a533-cb2fa63c205a%2F08f06734-cdb1-4647-b821-96850cb2fdef%2F7gy1d_processed.png&w=3840&q=75)
Transcribed Image Text:### Solving Systems of Equations
**Problem Statement:**
Solve the system of equations by any method.
\[
\begin{aligned}
6x + 11y &= 15 \\
x + 2y &= 4
\end{aligned}
\]
Enter the exact answer as an ordered pair, \((x, y)\).
If there is no solution, enter NS. If there is an infinite number of solutions, enter the general solution as an ordered pair in terms of \(x\).
---
### Explanation:
- **System of Equations:** A set of two or more equations that have common variables. Solving a system of equations means finding the values of the variables that satisfy all equations simultaneously.
- **Methods to Solve the System:**
- **Substitution Method:** Solve one of the equations for one variable and substitute this expression into the other equation.
- **Elimination Method:** Manipulate the equations to eliminate one variable, making it possible to solve for the remaining variable.
- **Graphical Method:** Graph the equations on a coordinate plane to find the point(s) of intersection.
- **Possible Outcomes:**
- A single solution \((x, y)\): The lines intersect at one point.
- No solution (NS): The lines are parallel and do not intersect.
- Infinite solutions: The lines coincide, meaning every point on one line is also on the other line.
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