Ответ:

46

Объяснение:

7z-4t=5/3

5z+3t=13/6

(z,t)=(1/3;1/6)

1/корень x-7=1/3

1/корень y+6=1/6

(x;y) = 16;30

подставляешь:

5/3 = 5/3

13/6=13/6

(x;y) = 16+30 = 46

[tex]\displaystyle\bf\\\left \{ {{\dfrac{7}{\sqrt{x-7} } -\dfrac{4}{\sqrt{y+6} }=\dfrac{5}{3} } \ |\cdot 3\atop {\dfrac{5}{\sqrt{x-7} } +\dfrac{3}{\sqrt{y+6} }=\dfrac{13}{6} } \ |\cdot 4} \right. \\\\\\+\left \{ {{\dfrac{21}{\sqrt{x-7} } -\dfrac{12}{\sqrt{y+6} }=5 } \atop {\dfrac{20}{\sqrt{x-7} } +\dfrac{12}{\sqrt{y+6} }=\dfrac{26}{3} } \ \right. \\------------\\\\\frac{41}{\sqrt{x-7} } =\frac{41}{3} \\\\\\\sqrt{x-7} =3\\\\x-7=9\\\\x=16[/tex]

[tex]\displaystyle\bf\\\frac{3}{\sqrt{y+6} } =\frac{13}{6} -\frac{5}{\sqrt{x-7} } =\frac{13}{6} -\frac{5}{3} =\frac{1}{2} \\\\\\\frac{3}{\sqrt{y+6} } =\frac{1}{2} \\\\\\\sqrt{y+6} =6\\\\y+6=36\\\\y=30\\\\\\\boxed{\boxed{x+y=16+30=46}}[/tex]