What is 2/x-3/y =9, 5/x+1/y =7 ?

The solution to 2/x-3/y =9, 5/x+1/y =7 is

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2/x-3/y =9, 5/x+1/y =7

\frac{2}{x} - \frac{3}{y} = 9, \frac{5}{x} + \frac{1}{y} = 7

(x = \frac{17}{30}, y = - \frac{17}{31})

Solution steps

[\frac{2}{x} - \frac{3}{y} = 9 \frac{5}{x} + \frac{1}{y} = 7]

Isolate

x

for

\frac{2}{x} - \frac{3}{y} = 9 : x = \frac{2 y}{3 ( 1 + 3 y )}; y \neq = - \frac{1}{3}

Plug the solutions

x = \frac{2 y}{3 ( 1 + 3 y )}

into

\frac{5}{x} + \frac{1}{y} = 7

For

\frac{5}{x} + \frac{1}{y} = 7

, subsitute

x

with

\frac{2 y}{3 ( 1 + 3 y )} : y = - \frac{17}{31}

Plug the solutions

y = - \frac{17}{31}

into

\frac{2}{x} - \frac{3}{y} = 9

For

\frac{2}{x} - \frac{3}{y} = 9

, subsitute

y

with

- \frac{17}{31} : x = \frac{17}{30}

Verify solutions by plugging them into the original equations

Therefore, the final solution for

\frac{2}{x} - \frac{3}{y} = 9, \frac{5}{x} + \frac{1}{y} = 7

(x = \frac{17}{30}, y = - \frac{17}{31})

y = 2 x + 9, 3 x + 2 y = 4

4 x - y = - 12, 4 x + 2 y = 0

31 (x + y) + 2 z = 21, 3 x - (y + z) = 6, 5 x + (x + y - z) = 38

3 x - y = 4, - y + 2 x = 1

5 x + 2 y = 24, 4 x + 3 y = 29