Competition problem — Algebra — Maths Olympiad Prep

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Algebra Difficulty 3.9 AMC 10/12 Find the answer Italy

Problem:

Two real numbers $a$ and $b$ are given such that $|3 a-b+1|=|b|$ . Then necessarily we have...

Pick one

Solution

Solution:

The answer is (E). Indeed, in the Cartesian plane having axes $a$ and $b$ , the region described by the equation $|3 a-b+1|=|b|$ is given by the union of the line $3 a+1=0$ and the line $3 a-2 b+1=0$ . Therefore none of the first four proposed answers is correct.

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Source: MathNet, licensed CC-BY-4.0. Statement translated into English from it; metadata (topic, difficulty) added by this project.