Consider systems of two linear equations with unknowns and ,
\begin{align*} a_1 x + b_1 y & = 0 \\ a_2 x + b_2 y & = 0 \end{align*}
where each of the coefficients is either or and the system has a solution other than . How many such systems of equations are there? (The equations in a system need not be distinct, and two systems containing the same equations in a different order are considered different.)
8
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12
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16
