$$\frac{x+2y}{4}-\frac{x-2y}{2}-\frac{x-2y}{3}=1-x; 3x-2y=8; 3x+6u-6x+12u-28-8u-1-x$$
$z=10u-\frac{435}{11}$
$$-7x+26y=12-12x$$ $$3x-2y=8$$ $$z=3x+6u-6x+12u-28-8u-1-x$$
$$x=\frac{12}{5}-\frac{26}{5}y$$
$$3\left(\frac{12}{5}-\frac{26}{5}y\right)-2y=8$$ $$z=3\left(\frac{12}{5}-\frac{26}{5}y\right)+6u-6\left(\frac{12}{5}-\frac{26}{5}y\right)+12u-28-8u-1-\left(\frac{12}{5}-\frac{26}{5}y\right)$$
$$y=-\frac{1}{22}$$ $$z=-\frac{193}{5}+\frac{104}{5}y+10u$$
$$z=-\frac{193}{5}+\frac{104}{5}\left(-\frac{1}{22}\right)+10u$$
$$z=-\frac{435}{11}+10u$$
$$x=\frac{12}{5}-\frac{26}{5}\left(-\frac{1}{22}\right)$$
$$x=\frac{29}{11}$$
$$x=\frac{29}{11}$$ $$y=-\frac{1}{22}$$ $$z=-\frac{435}{11}+10u$$
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