[tex]\left \{ {{x * y = 2000} \atop {(x+50)(y-2)=2000}} \right.[/tex]
[tex](x+50)(y-2)=xy\\xy+50y-2x-100=xy\\50y-2x-100=0\\-2x=100-50y\\x=25y-50[/tex]
[tex](25y-50)*y=2000\\25y^2-50y-2000=0\\y^2-2y-80=0[/tex]
[tex]\Delta = (-2)^2-4*1*(-80)=324\\\sqrt{\Delta} =\sqrt{324} = 18[/tex]
[tex]y=\frac{2\frac{+}{-} 18}{2} => y=10\ \lor\ y=-8[/tex]
[tex]x=25*(10)-50=200 \lor x=25*(-8)-50=-250[/tex]
[tex]\left \{ {{y=10} \atop {x=200}} \right. \lor \left \{ {{y=-8} \atop {x=-250}} \right.[/tex]
