Question

{54/(x+y)+48/x=6 {64/(x)-2=36/(x+y) решите систему уравнений!

Answer 1

ОДЗ:
x ≠ - y
x≠ 0

$\left \{ {{ \frac{54}{x + y} + \frac{48}{x} = 6 } \atop { \frac{64}{x} - 2 = \frac{36}{x + y} }} \right.$
Пусть $a = \frac{18}{x + y}$ и $b = \frac{16}{x}$.
$\left \{ {3a + 3b = 6{} \atop {4b - 2 = 2a}} \right.$
$\left \{ {a + b = 2{} \atop {2b - 1 = a}} \right.$
$\left \{ {2b - 1 + b = 2{} \atop {2b - 1 = a}} \right.$
$\left \{ {3b = 3{} \atop {2b - 1 = a}} \right.$
$\left \{ {b = 1 {} \atop {2*1 - 1 = a}} \right.$
$\left \{ {a = 1{} \atop {b = 1}} \right.$
Обратная замена:
$\left \{ {{ \frac{18}{x + y} = 1} \atop { \frac{16}{x} = 1}} \right.$
$\left \{ {{ \frac{18}{16 + y} = 1} \atop { x = 16}} \right.$
$\left \{ {{ {16 + y = 18} \atop { x = 16}} \right.$
$\left \{ {{y=2} \atop {x=16}} \right.$
ответ: $(16; 2).$