Х - первое число
y - второе число
составим систему уравнений
\left \{ {{xy=-24} \atop {x=13-2y}} \right. <=>\\\
\left \{ {{(13-2y)y=-24} \atop {x=13-2y}} \right. <=>\left \{ {{13y-2y^2+24=0} \atop {x=13-2y}} \right. \\\
-2y^2+13y+24=0\\\
D=169+192=361\\\
y_1=\frac{-13-19}{-2\cdot 2}=8\ \ \ \ \ \ \ y_2=\frac{-13+19}{-2\cdot 2}=-1,5\\\
x_1=13-2\cdot 8=-3\ \ \ \ \ \ \ \ \ \ x_2=13-2\cdot (-1,5)=16" alt=" \left \{ {{xy=-24} \atop {x+2y=13}} \right. <=>\left \{ {{xy=-24} \atop {x=13-2y}} \right. <=>\\\
\left \{ {{(13-2y)y=-24} \atop {x=13-2y}} \right. <=>\left \{ {{13y-2y^2+24=0} \atop {x=13-2y}} \right. \\\
-2y^2+13y+24=0\\\
D=169+192=361\\\
y_1=\frac{-13-19}{-2\cdot 2}=8\ \ \ \ \ \ \ y_2=\frac{-13+19}{-2\cdot 2}=-1,5\\\
x_1=13-2\cdot 8=-3\ \ \ \ \ \ \ \ \ \ x_2=13-2\cdot (-1,5)=16" align="absmiddle" class="latex-formula">
существуют две пары таких чисел
(-3; 8) и (16; -1,5)