Question

Решите систему ур-й
$\frac{1}{x} + \frac{2}{y} = 10 \\ \frac{3}{x} - \frac{4}{y} = 15$

Answer 1

$\left \{ {{\frac{1}{x} +\frac{2}{y} }=10|*(-3) \atop {\frac{3}{x}-\frac{4}{y} =15 }} \right.\\\\+\left \{ {{-\frac{3}{x}-\frac{6}{y}=-30} \atop {\frac{3}{x}-\frac{4}{y}=15}} \right.\\\\-------\\\\-\frac{10}{y} =-15\\\\y=\frac{10}{15}=\frac{2}{3}\\\\\frac{1}{x}+\frac{2}{\frac{2}{3} }=10\\\\\frac{1}{x}+3=10\\\\\frac{1}{x} =7\\\\x=\frac{1}{7}$

Ответ : $(\frac{1}{7};\frac{2}{3})$

Answer 2

Замена 1/x = a; 1/y = b

a + 2b = 10

3a - 4b = 15

Умножаем 1 уравнение на 2

2a + 4b = 20

3a - 4b = 15

Складываем уравнения

5a = 35; a = 35/5 = 7 = 1/x

b = (10 - a) /2 = (10 - 7)/2 = 3/2 = 1/y

x = 1/7; y = 2/3