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variabes are 4 , equations are 3 so i think data in adequate.
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$x_1+x_2=0$

Two variables, one equation, infinite solutions..

$x_1+2x_2-x_4=1\to(1)$

$-2x_1-3x_2+4x_3+5x_4=2\to(2)$

$2x_1+4x_2-2x_4=3\to(3)$

Do $eq(3)-2\times eq(1)$

$\implies 0=2$

Hence system of linear equations is inconsistent..

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Thanks.. :)