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

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

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

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

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

Solution steps

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

Isolate

x

for

\frac{2}{x} + \frac{3}{y} = 5 : x = - \frac{2 y}{3 - 5 y}; y \neq = \frac{3}{5}

Plug the solutions

x = - \frac{2 y}{3 - 5 y}

into

\frac{3}{x} - \frac{1}{y} = - 9

For

\frac{3}{x} - \frac{1}{y} = - 9

, subsitute

x

with

- \frac{2 y}{3 - 5 y} : y = \frac{1}{3}

Plug the solutions

y = \frac{1}{3}

into

\frac{2}{x} + \frac{3}{y} = 5

For

\frac{2}{x} + \frac{3}{y} = 5

, subsitute

y

with

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

Verify solutions by plugging them into the original equations

Therefore, the final solution for

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

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

3 x + 4 y = - 6, 2 x + 4 y = 16

8 y - 8 x = 30, 5 x - 12 y = 4

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

10 x + y = 51, 0 y + x = 14

3 y - 4 z = 8, 2 y - z = 9