1.) Which best describes a system of equations that has no solution?
•consistent, independent
•inconsistent, dependent
•consistent, dependent
•inconsistent*
ANSWER: D
Please check my answer, thank you!
1.- D
2.- C
3.- D
3.- B
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Thank you! @Steve
To determine which option describes a system of equations that has no solution, we need to understand the concepts of consistent, independent, inconsistent, and dependent systems.
A system of equations is said to be consistent if it has at least one solution, meaning the equations can be satisfied simultaneously. A system is inconsistent if it has no solutions, which means the equations contradict each other and cannot be satisfied simultaneously.
A system is considered independent when it has exactly one solution, with no dependencies or restrictions on the variables. On the other hand, a dependent system has infinitely many solutions, where the equations are not enough to determine a unique solution.
Based on these definitions, we can see that the correct answer is option (D) inconsistent. An inconsistent system is the only choice that indicates a lack of solutions.