AlgebraVery hardCondition for no solution
Algebra practice question
The system of equations 2x − y = 5 and 4x − 2y = c, where c is a constant, has no solution. Which of the following must be true?
- A. c ≠ 10Correct
- B. c = 10
- C. c = 5
- D. c ≠ 5
Answer: A. c ≠ 10
The second equation's left side is twice the first's. If c = 10 the equations describe the same line (infinitely many solutions); for any other c the lines are parallel and distinct — no solution. So c ≠ 10.
Why the other answers are wrong
- B. c = 10
- c = 10 gives the SAME line, hence infinitely many solutions.
- C. c = 5
- c = 5 is one value with no solution, but the condition that must hold is c ≠ 10.
- D. c ≠ 5
- c ≠ 5 allows c = 10, which gives infinitely many solutions rather than none.
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