# 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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