AlgebraHardSecond equation for infinitely many solutions
Algebra practice question
A system of two linear equations in x and y has infinitely many solutions. One of the equations is 3x − y = 7. Which of the following could be the other equation?
- A. 6x − 2y = 14Correct
- B. 6x − 2y = 7
- C. 3x + y = 7
- D. −3x + y = 7
Answer: A. 6x − 2y = 14
Infinitely many solutions means the two equations describe the same line — one is a multiple of the other. 6x − 2y = 14 is exactly 2 times 3x − y = 7.
Why the other answers are wrong
- B. 6x − 2y = 7
- The left side is doubled but the right side isn't: a parallel line, so NO solutions.
- C. 3x + y = 7
- 3x + y = 7 has a different slope (−3 instead of 3); the lines cross once.
- D. −3x + y = 7
- −3x + y = 7 is 3x − y = −7, parallel to the given line: no solutions.
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