What is 1/x+1/y =5, 3/x+2/y =12 ?

The solution to 1/x+1/y =5, 3/x+2/y =12 is

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1/x+1/y =5, 3/x+2/y =12

\frac{1}{x} + \frac{1}{y} = 5, \frac{3}{x} + \frac{2}{y} = 12

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

Solution steps

[\frac{1}{x} + \frac{1}{y} = 5 \frac{3}{x} + \frac{2}{y} = 12]

Isolate

x

for

\frac{1}{x} + \frac{1}{y} = 5 : x = - \frac{y}{1 - 5 y}; y \neq = \frac{1}{5}

Plug the solutions

x = - \frac{y}{1 - 5 y}

into

\frac{3}{x} + \frac{2}{y} = 12

For

\frac{3}{x} + \frac{2}{y} = 12

, subsitute

x

with

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

Plug the solutions

y = \frac{1}{3}

into

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

For

\frac{1}{x} + \frac{1}{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{1}{x} + \frac{1}{y} = 5, \frac{3}{x} + \frac{2}{y} = 12

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

10 x + 8 y = 6, e^{4} x - 9 y = 161

3 x - 7 y + 10 = 0, y - 2 x - 3 = 0

r = 0, s = 0

2 x - 8 y + 3 z = 1, - x + 2 y - 3 z = - 2

x + y = 2, x - y = - 6