Помогите решить систему уравнений и объясните решение [latex]3x-y=5[/latex][latex] \frac{x+y}{2} - \frac{2+y}{3} = \frac{1}{2} [/latex]

[latex] \left \{ {{3x-y=5} \atop {\frac{x+y}{2} - \frac{2+y}{3} = \frac{1}{2}}} \right. <=> \left \{ {{y=3x-5} \atop {3(x+y)-2(2+y)=3} \right. <=> \left \{ {{y=3x-5} \atop {3x+3y-4-2y=3} \right. <=> \\\ \left \{ {{y=3x-5} \atop {3x+y=7} \right. <=>\left \{ {{y=3x-5} \atop {3x+3x-5=7} \right. <=>\left \{ {{y=3x-5} \atop {6x=12} \right. <=>\\\ \left \{ {{y=3x-5} \atop {x=2} \right. <=>\left \{ {{y=3\cdot 2-5} \atop {x=2} \right. <=>\left \{ {{y=1} \atop {x=2} \right.[/latex]