Algebra practice question

Answer: A. 2x − y = 5 and 6x − 3y = 4

In choice A, the left sides are proportional (6x − 3y is 3 times 2x − y) but the right sides are not (4 is not 3 × 5). The lines are parallel and distinct, so they never meet.

Why the other answers are wrong

B. 2x − y = 5 and 6x − 3y = 15

6x − 3y = 15 is exactly 3 times 2x − y = 5 — the same line, so infinitely many solutions.

C. 2x − y = 5 and 2x + y = 5

These lines have slopes 2 and −2, so they cross once: (2.5, 0).

D. 2x − y = 5 and x + 3y = 4

These lines have slopes 2 and −1/3, so they cross once.

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