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, 2003

Algebra Difficulty 2.0 Junior Prove it Canada

Suppose that the functions $f(x)$ and $g(x)$ satisfy the system of equations
$f(x)+3g(x)=x^2+x+6$
$2f(x)+4g(x)=2x^2+4$
for all $x$ . Determine the values of $x$ for which $f(x)=g(x)$ .

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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. Solutions are the publisher's, linked not copied.