Algebra · Absolute value equations · Parameter · Systems of equations · Graphs in the plane
For which values of the parameter \(a\) does the system of equations
\[ |x - 1| + |y - a| = 1 , \qquad y = -2|x - 1| - 1 \]
have exactly three solutions \((x, y)\)?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), izbirno (selection) round 2005, 1. letnik, category A, problem 2. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source