Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. System A -3x+y=6 3x-y=6 System B -4x+y=-4 4x−y=4 The system has no solution. The system has a unique solution: (x, y) = (₂0) The system has infinitely many solutions. They must satisfy the following equation: y = 0 The system has no solution. The system has a unique solution: (x, y) = (₂0) The system has infinitely many solutions. They must satisfy the following equation: y=
Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution. System A -3x+y=6 3x-y=6 System B -4x+y=-4 4x−y=4 The system has no solution. The system has a unique solution: (x, y) = (₂0) The system has infinitely many solutions. They must satisfy the following equation: y = 0 The system has no solution. The system has a unique solution: (x, y) = (₂0) The system has infinitely many solutions. They must satisfy the following equation: y=
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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![### Solving Systems of Linear Equations
Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution.
#### System A
\[
\begin{cases}
-3x + y = 6 \\
3x - y = 6
\end{cases}
\]
Options:
1. ⃝ The system has no solution.
2. ⃝ The system has a unique solution:
\[
(x, y) = \left[ \ \ , \ \ \right]
\]
3. ⃝ The system has infinitely many solutions.
They must satisfy the following equation:
\[
y = \left[ \ \ \right]
\]
#### System B
\[
\begin{cases}
-4x + y = -4 \\
4x - y = 4
\end{cases}
\]
Options:
1. ⃝ The system has no solution.
2. ⃝ The system has a unique solution:
\[
(x, y) = \left[ \ \ , \ \ \right]
\]
3. ⃝ The system has infinitely many solutions.
They must satisfy the following equation:
\[
y = \left[ \ \ \right]
\]
For each system, examine the provided equations, determine the nature of their solutions and provide the detailed steps to find the solutions.
- If the lines represented by the equations are parallel but not coincident, the system has no solution.
- If the lines intersect at a single point, the system has a unique solution.
- If the lines are coincident, the system has infinitely many solutions, and we must provide the equation that represents the line.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F277ae00b-d056-42ed-a729-386f4fca5973%2Fcb11edb7-d5ec-4bf0-aebf-2643f4e0c3c8%2F7oczls_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Solving Systems of Linear Equations
Two systems of equations are given below. For each system, choose the best description of its solution. If applicable, give the solution.
#### System A
\[
\begin{cases}
-3x + y = 6 \\
3x - y = 6
\end{cases}
\]
Options:
1. ⃝ The system has no solution.
2. ⃝ The system has a unique solution:
\[
(x, y) = \left[ \ \ , \ \ \right]
\]
3. ⃝ The system has infinitely many solutions.
They must satisfy the following equation:
\[
y = \left[ \ \ \right]
\]
#### System B
\[
\begin{cases}
-4x + y = -4 \\
4x - y = 4
\end{cases}
\]
Options:
1. ⃝ The system has no solution.
2. ⃝ The system has a unique solution:
\[
(x, y) = \left[ \ \ , \ \ \right]
\]
3. ⃝ The system has infinitely many solutions.
They must satisfy the following equation:
\[
y = \left[ \ \ \right]
\]
For each system, examine the provided equations, determine the nature of their solutions and provide the detailed steps to find the solutions.
- If the lines represented by the equations are parallel but not coincident, the system has no solution.
- If the lines intersect at a single point, the system has a unique solution.
- If the lines are coincident, the system has infinitely many solutions, and we must provide the equation that represents the line.
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