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Which of the following conditions holds true for a system of equations to be consistent?
- a)It should have one or more solutions
- b)It should have no solutions
- c)It should have exactly one solution
- d)It should have exactly two solutions
Correct answer is option 'A'. Can you explain this answer?
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Which of the following conditions holds true for a system of equations...
If a given system of equations has one or more solutions then the system is said to be consistent.
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Which of the following conditions holds true for a system of equations...
Consistency of a System of Equations
There are three main possibilities for a system of equations to be consistent: having one or more solutions, having no solutions, or having exactly one solution. Let's discuss why having one or more solutions makes a system of equations consistent.
Explanation:
1. Definition of Consistency:
- A system of equations is considered consistent if it has at least one solution. This means that there is a set of values for the variables that satisfy all the equations in the system.
2. Importance of Having One or More Solutions:
- If a system of equations has one or more solutions, it means that the equations intersect at one or more points, indicating that the system is solvable.
- Having solutions implies that the equations are not contradictory and can be satisfied simultaneously, making the system consistent.
3. Implications of Having No Solutions or Exactly One Solution:
- If a system of equations has no solutions, it means that the equations are parallel and never intersect, leading to inconsistency.
- Similarly, if a system has exactly one solution, it means that the equations intersect at a single point, making the system consistent but restrictive.
Conclusion:
- In summary, a system of equations is considered consistent when it has one or more solutions. This condition ensures that the equations are not contradictory and can be simultaneously satisfied, making the system solvable.
There are three main possibilities for a system of equations to be consistent: having one or more solutions, having no solutions, or having exactly one solution. Let's discuss why having one or more solutions makes a system of equations consistent.
Explanation:
1. Definition of Consistency:
- A system of equations is considered consistent if it has at least one solution. This means that there is a set of values for the variables that satisfy all the equations in the system.
2. Importance of Having One or More Solutions:
- If a system of equations has one or more solutions, it means that the equations intersect at one or more points, indicating that the system is solvable.
- Having solutions implies that the equations are not contradictory and can be satisfied simultaneously, making the system consistent.
3. Implications of Having No Solutions or Exactly One Solution:
- If a system of equations has no solutions, it means that the equations are parallel and never intersect, leading to inconsistency.
- Similarly, if a system has exactly one solution, it means that the equations intersect at a single point, making the system consistent but restrictive.
Conclusion:
- In summary, a system of equations is considered consistent when it has one or more solutions. This condition ensures that the equations are not contradictory and can be simultaneously satisfied, making the system solvable.
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Which of the following conditions holds true for a system of equations to be consistent?a)It should have one or more solutionsb)It should have no solutionsc)It should have exactly one solutiond)It should have exactly two solutionsCorrect answer is option 'A'. Can you explain this answer?
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Which of the following conditions holds true for a system of equations to be consistent?a)It should have one or more solutionsb)It should have no solutionsc)It should have exactly one solutiond)It should have exactly two solutionsCorrect answer is option 'A'. Can you explain this answer? for Class 12 2024 is part of Class 12 preparation. The Question and answers have been prepared according to the Class 12 exam syllabus. Information about Which of the following conditions holds true for a system of equations to be consistent?a)It should have one or more solutionsb)It should have no solutionsc)It should have exactly one solutiond)It should have exactly two solutionsCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for Class 12 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Which of the following conditions holds true for a system of equations to be consistent?a)It should have one or more solutionsb)It should have no solutionsc)It should have exactly one solutiond)It should have exactly two solutionsCorrect answer is option 'A'. Can you explain this answer?.
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