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MathNet 2018-part-03 — 181 problems (EN–VI) Question 115

Math Olympiad Vault · MathNet 2018-part-03 — 181 problems (EN–VI)

Question 115

Solve, depending on the values of the real parameter $a$, the system of equations
$$
\left\{
\begin{array}{l}
y-4 = a(x-2), \\
\dfrac{2y}{x+|x|} = \sqrt{y}
\end{array}
\right.
$$
in $\mathbb{R} \times \mathbb{R}$.