What is 2/x+3/y =6, 4/x+5/y =9 ?

The solution to 2/x+3/y =6, 4/x+5/y =9 is

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2/x+3/y =6, 4/x+5/y =9

\frac{2}{x} + \frac{3}{y} = 6, \frac{4}{x} + \frac{5}{y} = 9

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

Solution steps

[\frac{2}{x} + \frac{3}{y} = 6 \frac{4}{x} + \frac{5}{y} = 9]

Isolate

x

for

\frac{2}{x} + \frac{3}{y} = 6 : x = - \frac{2 y}{3 ( 1 - 2 y )}; y \neq = \frac{1}{2}

Plug the solutions

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

into

\frac{4}{x} + \frac{5}{y} = 9

For

\frac{4}{x} + \frac{5}{y} = 9

, subsitute

x

with

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

Plug the solutions

y = \frac{1}{3}

into

\frac{2}{x} + \frac{3}{y} = 6

For

\frac{2}{x} + \frac{3}{y} = 6

, subsitute

y

with

\frac{1}{3} : x = - \frac{2}{3}

Verify solutions by plugging them into the original equations

Therefore, the final solution for

\frac{2}{x} + \frac{3}{y} = 6, \frac{4}{x} + \frac{5}{y} = 9

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

6 x + 4 y = 3, 5 x - 102 y = 2

16 x + 5 y = 8, 22 x + 2 y = - 28

4 x + 2 y = 4, 2 x - 3 y = 7

x - 3 y = 5, 2 x + 2 y = 4

x + y + 3 z = 10, x - y - z = - 2, 2 x + 3 y + 4 z = 4