College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.2: Guassian Elimination And Matrix Methods
Problem 93E
Related questions
Question
25
![**Solving a System of Equations Using Augmented Matrix Methods**
Consider the following system of equations:
\[
\begin{aligned}
x_1 - 2x_2 &= -7 \\
2x_1 - x_2 &= 1
\end{aligned}
\]
To solve the system using augmented matrix methods, we form the augmented matrix and reduce it to echelon form.
---
**Question:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
**Options:**
- **A.** The unique solution to the system is \( x_1 = \_\_\_\_\) and \( x_2 = \_\_\_\_\). (Simplify your answers.)
- **B.** There are infinitely many solutions. The solution is \( x_1 = \_\_\_\_\) and \( x_2 = t \), for any real number \( t \). (Type an expression using \( t \) as the variable.)
- **C.** There is no solution.
---
Choose the correct option to identify the nature of the solution for this system of equations. If the system has a unique solution or infinitely many solutions, provide the simplified expressions or general forms of the solutions accordingly.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F8df1a74e-b29a-4337-9f07-a3244c840179%2F76dab370-93d6-4dda-96e6-1aca4edfd3cb%2Fm0gcf2k_processed.png&w=3840&q=75)
Transcribed Image Text:**Solving a System of Equations Using Augmented Matrix Methods**
Consider the following system of equations:
\[
\begin{aligned}
x_1 - 2x_2 &= -7 \\
2x_1 - x_2 &= 1
\end{aligned}
\]
To solve the system using augmented matrix methods, we form the augmented matrix and reduce it to echelon form.
---
**Question:**
Select the correct choice below and, if necessary, fill in the answer box to complete your choice.
**Options:**
- **A.** The unique solution to the system is \( x_1 = \_\_\_\_\) and \( x_2 = \_\_\_\_\). (Simplify your answers.)
- **B.** There are infinitely many solutions. The solution is \( x_1 = \_\_\_\_\) and \( x_2 = t \), for any real number \( t \). (Type an expression using \( t \) as the variable.)
- **C.** There is no solution.
---
Choose the correct option to identify the nature of the solution for this system of equations. If the system has a unique solution or infinitely many solutions, provide the simplified expressions or general forms of the solutions accordingly.
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