Решите систему: [latex] \left \{ {{|x-1|+|y-5|=1} \atop {y=5+|x-1|}} \right. [/latex]

[latex] \left \{ {{|x-1|+|y-5|=1} \atop {y=5+|x-1|}} \right. \\\ |x-1|=y-5 \\\ y-5+|y-5|=1 \\\ \left \{ {{y-5+y-5=1, y \geq 5} \atop {{y-5+5-y=1, y< 5}} \right. \\\ \left \{ {{2y=11, y \geq 5} \atop {{0 \neq 1, y< 5}} \right. \\\ y=5,5 \\\ y=5+|x-1| \\\ 5.5=5+|x-1| \\\ |x-1|=0.5 \\\ \left \{ {{x-1=0.5} \atop {x-1=-0.5}} \right. \\\ x_1=1.5 \\\ x_2=0.5[/latex] Ответ: (1,5; 5,5); (0,5; 5,5)