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Wouldn't it have been much easier to make x=4-y and substitute that into xy=12 and xy=4? Then 4y-y^2=12 which becomes -y^2+4y-12=0 which becomes y^2-4y+12=0, and solve by quadratic equation. Similarly, 4y-y^2=4, which becomes - y^2+4y-4=0, which becomes y^2-4y+4=0, which becomes (y-2)(y-2)=0, which solves to y=2, therefore 2x=4, and x also =2.
Largo, pero muy explicado, aunque, confieso, una parte final no la capte en su definición. GUARDARÉ EL EJERCICIO Y LO VERÉ E INTENTARÉ, INTERPRETAR EL PASO A PASO. GRACIAS POR ENSEÑAR.