What is 1/x+1/y =1, 2/x-3/y =-13 ?

The solution to 1/x+1/y =1, 2/x-3/y =-13 is

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1/x+1/y =1, 2/x-3/y =-13

\frac{1}{x} + \frac{1}{y} = 1, \frac{2}{x} - \frac{3}{y} = - 13

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

Solution steps

[\frac{1}{x} + \frac{1}{y} = 1 \frac{2}{x} - \frac{3}{y} = - 13]

Isolate

x

for

\frac{1}{x} + \frac{1}{y} = 1 : x = - \frac{y}{1 - y}; y \neq = 1

Plug the solutions

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

into

\frac{2}{x} - \frac{3}{y} = - 13

For

\frac{2}{x} - \frac{3}{y} = - 13

, subsitute

x

with

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

Plug the solutions

y = \frac{1}{3}

into

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

For

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

, 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{1}{x} + \frac{1}{y} = 1, \frac{2}{x} - \frac{3}{y} = - 13

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

- 10 x - 2 y = 12, - 7 x - 4 y = - 15

2 x + 3 y = 25, 4 x - y = 15

x + 7 y = 8, 3 x + 2 y = 5

2 x + y = 23, 4 x - y = 19

- 4 y = - 11, 5 x + 6 y = 7