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5x 7y %3D a. 5x + 7y = O Infinitely many solutions O No Solution O Unique solution - 5 7x b. 3y 19x 8y = - 3 O No Solution O Unique solution OInfinitely many solutions 3y 8 C. 91 24

5x 7y %3D a. 5x + 7y = O Infinitely many solutions O No Solution O Unique solution - 5 7x b. 3y 19x 8y = - 3 O No Solution O Unique solution OInfinitely many solutions 3y 8 C. 91 24

Algebra and Trigonometry (6th Edition)
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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### Determining the Number of Solutions for Systems of Linear Equations A linear system may have a unique solution, no solution, or infinitely many solutions. Determine the number of solutions for each of the following systems. #### a. \[ \begin{cases} 5x - 7y = -7 \\ -5x + 7y = 9 \end{cases} \] - ☐ Infinitely many solutions - ☐ No Solution - ☐ Unique solution #### b. \[ \begin{cases} 7x - 3y = -5 \\ 19x - 8y = -3 \end{cases} \] - ☐ No Solution - ☐ Unique solution - ☐ Infinitely many solutions #### c. \[ \begin{cases} -3x + 3y = 8 \\ 9x - 9y = -24 \end{cases} \] - ☐ No Solution - ☐ Unique solution - ☐ Infinitely many solutions Analyze each system to determine the number of solutions. The possibilities for the number of solutions are: - **Infinitely many solutions**: The equations represent the same line. - **No solution**: The lines are parallel and distinct. - **Unique solution**: The lines intersect at a single point.
Transcribed Image Text:### Determining the Number of Solutions for Systems of Linear Equations A linear system may have a unique solution, no solution, or infinitely many solutions. Determine the number of solutions for each of the following systems. #### a. \[ \begin{cases} 5x - 7y = -7 \\ -5x + 7y = 9 \end{cases} \] - ☐ Infinitely many solutions - ☐ No Solution - ☐ Unique solution #### b. \[ \begin{cases} 7x - 3y = -5 \\ 19x - 8y = -3 \end{cases} \] - ☐ No Solution - ☐ Unique solution - ☐ Infinitely many solutions #### c. \[ \begin{cases} -3x + 3y = 8 \\ 9x - 9y = -24 \end{cases} \] - ☐ No Solution - ☐ Unique solution - ☐ Infinitely many solutions Analyze each system to determine the number of solutions. The possibilities for the number of solutions are: - **Infinitely many solutions**: The equations represent the same line. - **No solution**: The lines are parallel and distinct. - **Unique solution**: The lines intersect at a single point.
### Solving Systems of Linear Equations #### Problem d Given the system: \[ \begin{cases} -4x + 4y = -9 \\ -20x + 20y = 2 \end{cases} \] Determine the type of solution this system has: - Unique solution - No solution - Infinitely many solutions #### Problem e Given the system: \[ \begin{cases} x - 5y = -4 \\ 4x - 20y = -16 \end{cases} \] Determine the type of solution this system has: - Unique solution - Infinitely many solutions - No solution ### Instructions Review each system of equations and select the correct type of solution from the options provided. After you have made your selections for both problems, click the "Next Question" button to proceed to the next set of exercises.
Transcribed Image Text:### Solving Systems of Linear Equations #### Problem d Given the system: \[ \begin{cases} -4x + 4y = -9 \\ -20x + 20y = 2 \end{cases} \] Determine the type of solution this system has: - Unique solution - No solution - Infinitely many solutions #### Problem e Given the system: \[ \begin{cases} x - 5y = -4 \\ 4x - 20y = -16 \end{cases} \] Determine the type of solution this system has: - Unique solution - Infinitely many solutions - No solution ### Instructions Review each system of equations and select the correct type of solution from the options provided. After you have made your selections for both problems, click the "Next Question" button to proceed to the next set of exercises.
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