Question

You are given the two equations \[ \left.\begin{array}{c} a y+x+b=0 \\ -5 y-3 x+7=0 \end{array}\right\} \] where \( a \) and \( b \) are constants. For each of the following statements, decide if it is always, sometimes or never true. For those which you decide are "sometimes" true, give examples of values for \( a \) and \( b \) which make the statement true. 1. The system (*) has no solutions. (Clear my choice) If you think "sometimes" then give an example: \( a= \) ? \( b= \) ? 2. The system (*) has precisely one solution. (Clear my choice) If you think "sometimes" then give an example: \( a= \) ? \( b= \) ? 3. The system (*) has precisely two solutions. (Clear my choice) If you think "sometimes" then give an example: \( a= \) ? \( b= \) ? 4. The system (*) has infinitely many solutions. ? (Clear my choice) If you think "sometimes" then give an example: \( a= \) ? \( b= \) ?

          You are given the two equations
\[
\left.\begin{array}{c}
a y+x+b=0 \\
-5 y-3 x+7=0
\end{array}\right\}
\]
where \( a \) and \( b \) are constants.
For each of the following statements, decide if it is always, sometimes or never true.
For those which you decide are "sometimes" true, give examples of values for \( a \) and \( b \) which make the statement true.
1. The system (*) has no solutions.

(Clear my choice)

If you think "sometimes" then give an example: \( a= \) ? \( b= \) ?
2. The system (*) has precisely one solution. (Clear my choice)

If you think "sometimes" then give an example: \( a= \) ? \( b= \) ?
3. The system (*) has precisely two solutions. (Clear my choice)

If you think "sometimes" then give an example: \( a= \) ? \( b= \) ?
4. The system (*) has infinitely many solutions. ? (Clear my choice)

If you think "sometimes" then give an example: \( a= \) ? \( b= \) ?
        
Show more…
You are given the two equations

    .
        a y+x+b=0 
        
        -5 y-3 x+7=0
    }

where a and b are constants.
For each of the following statements, decide if it is always, sometimes or never true.
For those which you decide are "sometimes" true, give examples of values for a and b which make the statement true.
1. The system (*) has no solutions.

(Clear my choice)

If you think "sometimes" then give an example: a= ? b= ?
2. The system (*) has precisely one solution. (Clear my choice)

If you think "sometimes" then give an example: a= ? b= ?
3. The system (*) has precisely two solutions. (Clear my choice)

If you think "sometimes" then give an example: a= ? b= ?
4. The system (*) has infinitely many solutions. ? (Clear my choice)

If you think "sometimes" then give an example: a= ? b= ?

Added by Stephen C.

Close

Elementary and Intermediate Algebra
Elementary and Intermediate Algebra
Marvin L. Bittinger, David J.… 4th Edition
Chapter 4
AceChat toggle button
Close icon
Ace pointing down

Please give Ace some feedback

Your feedback will help us improve your experience

Thumb up icon Thumb down icon
Thanks for your feedback!
Profile picture
You are given the two equations \[ \left.\begin{array}{c} a y+x+b=0 \\ -5 y-3 x+7=0 \end{array}\right\} \] where \( a \) and \( b \) are constants. For each of the following statements, decide if it is always, sometimes or never true. For those which you decide are "sometimes" true, give examples of values for \( a \) and \( b \) which make the statement true. 1. The system (*) has no solutions. (Clear my choice) If you think "sometimes" then give an example: \( a= \) □ \( b= \) □ 2. The system (*) has precisely one solution. (Clear my choice) If you think "sometimes" then give an example: \( a= \) □ \( b= \) □ 3. The system (*) has precisely two solutions. (Clear my choice) If you think "sometimes" then give an example: \( a= \) □ \( b= \) □ 4. The system (*) has infinitely many solutions. □ (Clear my choice) If you think "sometimes" then give an example: \( a= \) □ \( b= \) □
Close icon
Play audio
Feedback
Powered by NumerAI
David Collins Jennifer Stoner
Ivan Kochetkov verified

Adi S and 71 other subject Calculus 1 / AB educators are ready to help you.

Ask a new question

*

Labs

-

Want to see this concept in action?

NEW

Explore this concept interactively to see how it behaves as you change inputs.

View Labs

*

Key Concepts

-
Key Concept
Premium Feature
Explore the core concept behind this problem.
Play button
Key Concept
Premium Feature
Explore the core concept behind this problem.
Your browser does not support the video tag.

*

Recommended Videos

-
question-5-10-points-determine-the-values-of-for-which-the-following-system-of-linear-equations-has-no-solutions-unique-solution-or-infinitely-many-solutions-you-can-select-always-never-a-or-21577

Question 5 [10 points] Determine the values of a for which the following system of linear equations has no solutions, a unique solution, or infinitely many solutions. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. 3x1-9x2+3x3 = 0 -x1+8x2+ax3 = 0 -x1+6x2-x3 = 0 No Solutions: Always Unique Solution: Always Infinitely Many Solutions: Always Never When a = When a ≠

Adi S.

17-in-the-equations-6x-12ya-and-3x-6yba-and-b-are-constants-the-two-equations-have-infinitely-many-solutions-which-statements-are-true-mark-all-that-apply-a-if-a5b10-b-if-a18b9-c-if-a8b4-41442

In the equations 6x - 12y = a and 3x - 6y = b, a and b are constants. The two equations have infinitely many solutions. Which statements are true? Mark all that apply. A) If a = 5, b = 10. B) If a = 18, b = 9. C) If a = 8, b = 4.

Khushbu R.

solve-each-system-using-the-substitution-method-if-a-system-has-an-infinite-number-of-solutions-us-7

Solve each system using the substitution method. If a system has an infinite number of solutions, use set-builder notation to write the solution set. If a system has no solution, state this. $$ \begin{aligned} a &=-4 b \\ a+5 b &=5 \end{aligned} $$

Elementary and Intermediate Algebra

Systems of Equations in Two Variables

Systems of Equations and Substitution


*

Recommended Textbooks

-
Calculus: Early Transcendentals

Calculus: Early Transcendentals

James Stewart 8th Edition
achievement 1,948 solutions
Calculus: Early Transcendentals

Calculus: Early Transcendentals

William Briggs, Lyle Cochran, Bernard Gillet 3rd Edition
achievement 1,872 solutions
Thomas Calculus

Thomas Calculus

George B. Thomas Jr. 14th Edition
achievement 1,285 solutions
Need help? Use Ace
Ace is your personal tutor. It breaks down any question with clear steps so you can learn.
Start Using Ace
Ace is your personal tutor for learning
Step-by-step explanations
Instant summaries
Summarize YouTube videos
Understand textbook images or PDFs
Study tools like quizzes and flashcards
Listen to your notes as a podcast
Continue solving this problem
Create a free account to:
  • View full step-by-step solution
  • Ask follow-up questions with Ace AI
  • Save progress and study later
Continue Free
Join the community

18,000,000+

Students on Numerade


Trusted by students at 8,000+ universities

Numerade

Get step-by-step video solution
from top educators

Continue with Clever
or



By creating an account, you agree to the Terms of Service and Privacy Policy
Already have an account? Log In

A free answer
just for you

Watch the video solution with this free unlock.

Numerade

Log in to watch this video
...and 100,000,000 more!


EMAIL

PASSWORD

OR
Continue with Clever