Ответ: x₁y₁+x₂y₂=23.

Объяснение:

[tex]\displaystyle\\\left \{ {{y-x=2} \atop {xy-y=10}} \right.\ \ \ \ \left \{ {{x=y-2} \atop {y*(x-1)=10}} \right. \ \ \ \ \left \{ {{x=y-2} \atop {y*(y-2-1)=10}} \right. \ \ \ \ \left \{ {{x=y-2} \atop {y^2-3y-10=0}} \right.\\\\\\\left \{ {{x=y-2} \atop {y^2-5y+2y-10=0}} \right. \ \ \ \ \left \{ {{x=y-2} \atop {y*(y-5)+2*(y-5)=0}} \right. \ \ \ \ \left \{ {{x=y-2} \atop {(y-5)*(y+2)=0}} \right. \\\\\\\left \{ {{x_1=3\ \ \ \ x_2=-4} \atop {y_1=5\ \ \ \ y_2=-2}} \right.\ \ \ \ \ \ \ \ \Rightarrow[/tex]

[tex]x_1y_1+x_2y_2=3*5+(-4)*(-2)=15+8=23.[/tex]