Maths Olympiad Prep

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, 2012

Algebra Difficulty 1.3 Junior Find the answer Canada

If y=1y=1 and 4x2y+3=3x+3y4x-2y+3=3x+3y, what is the value of xx?

Pick one

Solution

Substituting y=1y=1 into the second equation, we obtain 4x2(1)+3=3x+3(1)4x-2(1)+3=3x+3(1).

Simplifying, we obtain 4x2+3=3x+34x-2+3=3x+3 or 4x+1=3x+34x+1=3x+3.

Therefore, 4x3x=314x-3x=3-1 or x=2x=2.

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.