2005 AMC 12A Problem 2

Below is the professionally curated solution for Problem 2 of the 2005 AMC 12A, from LIVE by Po-Shen Loh. You can also try the full timed exam, view all 2005 AMC 12A solutions, or check the answer key.

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Concepts:linear equationsubstitution

Difficulty rating: 910

2.

The equations 2x+7=32x + 7 = 3 and bx10=2bx - 10 = -2 have the same solution for x.x. What is the value of b?b?

8-8

4-4

2-2

44

88

Solution:

Solving 2x+7=32x + 7 = 3 gives x=2.x = -2.

Substituting into the second equation, 2b10=2,-2b - 10 = -2, so 2b=8-2b = 8 and b=4.b = -4.

Thus, the correct answer is B.

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