# Consistent ?? Think again

Algebra Level pending

$\begin{cases} x_1 +x_3=1 \\ -x_2+2x_3=\omega \\ x_1 - x_2 + 3x_3=2 \\ x_1+x_2-x_3 =1-\omega \end{cases}$

Consider the linear systems above, where $$\omega$$ is an arbitrary real constant.

Determine the value(s) of $$\omega$$ that results in a consistent system.

Note: If there's more than one value of $$\omega$$, then submit their sum as your answer.

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