2005 AMC 12A Problem 2

Problem 2 of 25EasierAlgebra

The equations

2x + 7 = 3

and

bx - 10 = -2

have the same solution for

x.

What is the value of

b?

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Solution

Solving

2x + 7 = 3

gives

x = -2.

Substituting into the second equation,

-2b - 10 = -2,

-2b = 8

and

b = -4.

Thus, the correct answer is B.

Concepts: linear equation · substitution

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.