$$2y+7x=-5; 5y-7x=12; x=; y=$$
$z=-1$
$$z=x$$ $$5y-7x=12$$ $$2y+7x=-5$$
$$x=z$$
$$5y-7z=12$$ $$2y+7z=-5$$
$$y=\frac{7}{5}z+\frac{12}{5}$$ $$z=-\frac{2}{7}y-\frac{5}{7}$$
$$z=-\frac{2}{7}\left(\frac{7}{5}z+\frac{12}{5}\right)-\frac{5}{7}$$
$$z=-1$$
$$y=\frac{7}{5}\left(-1\right)+\frac{12}{5}$$
$$y=1$$
$$x=-1$$
$$y=1$$ $$x=-1$$ $$z=-1$$
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