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A system of linear equations is said to be consistent, if it has
- a)at least one solution
- b)two solutions
- c)one solution
- d)no solution
Correct answer is option 'A'. Can you explain this answer?
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Consistency of a System of Linear Equations
Definition: A system of linear equations is said to be consistent if it has at least one solution, meaning there exists a set of values for the variables that satisfies all the equations in the system.
Explanation:
In a system of linear equations, we have multiple equations with multiple variables. The goal is to find the values of the variables that satisfy all the equations simultaneously.
There are three possibilities for the consistency of a system of linear equations:
1. Consistent System: A system of linear equations is consistent when there is at least one solution that satisfies all the equations. In other words, there exists a set of values for the variables that makes all the equations true.
2. Inconsistent System: A system of linear equations is inconsistent when there is no solution that satisfies all the equations. In other words, the equations are contradictory and cannot be solved simultaneously.
3. Dependent System: A system of linear equations is dependent when it has infinitely many solutions. In other words, the equations are not contradictory, but there are multiple sets of values for the variables that satisfy all the equations.
Explanation of the Options:
a) At least one solution: This option is correct because a consistent system must have at least one solution. It means there exists a set of values for the variables that satisfy all the equations in the system.
b) Two solutions: This option is not correct because a consistent system can have either a unique solution or infinitely many solutions. It is not limited to exactly two solutions.
c) One solution: This option is not specific enough because a consistent system can have either a unique solution or infinitely many solutions. It is not limited to exactly one solution.
d) No solution: This option is incorrect because a system with no solution is inconsistent, not consistent. A consistent system must have at least one solution.
Therefore, the correct answer is option 'a' - at least one solution.
Definition: A system of linear equations is said to be consistent if it has at least one solution, meaning there exists a set of values for the variables that satisfies all the equations in the system.
Explanation:
In a system of linear equations, we have multiple equations with multiple variables. The goal is to find the values of the variables that satisfy all the equations simultaneously.
There are three possibilities for the consistency of a system of linear equations:
1. Consistent System: A system of linear equations is consistent when there is at least one solution that satisfies all the equations. In other words, there exists a set of values for the variables that makes all the equations true.
2. Inconsistent System: A system of linear equations is inconsistent when there is no solution that satisfies all the equations. In other words, the equations are contradictory and cannot be solved simultaneously.
3. Dependent System: A system of linear equations is dependent when it has infinitely many solutions. In other words, the equations are not contradictory, but there are multiple sets of values for the variables that satisfy all the equations.
Explanation of the Options:
a) At least one solution: This option is correct because a consistent system must have at least one solution. It means there exists a set of values for the variables that satisfy all the equations in the system.
b) Two solutions: This option is not correct because a consistent system can have either a unique solution or infinitely many solutions. It is not limited to exactly two solutions.
c) One solution: This option is not specific enough because a consistent system can have either a unique solution or infinitely many solutions. It is not limited to exactly one solution.
d) No solution: This option is incorrect because a system with no solution is inconsistent, not consistent. A consistent system must have at least one solution.
Therefore, the correct answer is option 'a' - at least one solution.
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A system of linear equations is said to be consistent, if it hasa)at least one solutionb)two solutionsc)one solutiond)no solutionCorrect answer is option 'A'. Can you explain this answer?
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