AlgebraEasy–MediumRecognizing an equation of the same line
Algebra practice question
A system consists of the equation 2x − y = 5 and one equation below. Which choice creates a system with infinitely many solutions?
- A. 4x − 2y = 10Correct
- B. 4x − 2y = 5
- C. 4x + 2y = 10
- D. 2x + y = 5
Answer: A. 4x − 2y = 10
Doubling every term of 2x − y = 5 gives 4x − 2y = 10 — the same line, so every point on it solves the system.
Why the other answers are wrong
- B. 4x − 2y = 5
- The left side doubles but the right side does not: parallel distinct lines, no solutions.
- C. 4x + 2y = 10
- The sign of the y-term changed, so this is a different line that crosses the first exactly once.
- D. 2x + y = 5
- The y-sign differs from the given equation; the two lines intersect at a single point.
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