A War with Modulus

Algebra Level 4

If the number of common points satisfying the following equations

\[\begin{eqnarray} \|x|-|y\|&=&1 \\ 2 a|x\|y|+1&=&2 |x|+a |y| \end{eqnarray} \]

is \(8\), find the value of \(3a \), where \(a<1\).

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