What is 1/((7x))+1/((6y))=3, 1/((2x))-1/((3y))=5 ?

The solution to 1/((7x))+1/((6y))=3, 1/((2x))-1/((3y))=5 is

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1/((7x))+1/((6y))=3, 1/((2x))-1/((3y))=5

\frac{1}{( 7 x )} + \frac{1}{( 6 y )} = 3, \frac{1}{( 2 x )} - \frac{1}{( 3 y )} = 5

(x = \frac{1}{14}, y = \frac{1}{6})

Solution steps

[\frac{1}{( 7 x )} + \frac{1}{( 6 y )} = 3 \frac{1}{( 2 x )} - \frac{1}{( 3 y )} = 5]

Isolate

x

for

\frac{1}{( 7 x )} + \frac{1}{( 6 y )} = 3 : x = - \frac{6 y}{7 ( 1 - 18 y )}; y \neq = \frac{1}{18}

Plug the solutions

x = - \frac{6 y}{7 ( 1 - 18 y )}

into

\frac{1}{( 2 x )} - \frac{1}{( 3 y )} = 5

For

\frac{1}{( 2 x )} - \frac{1}{( 3 y )} = 5

, subsitute

x

with

- \frac{6 y}{7 ( 1 - 18 y )} : y = \frac{1}{6}

Plug the solutions

y = \frac{1}{6}

into

\frac{1}{( 7 x )} + \frac{1}{( 6 y )} = 3

For

\frac{1}{( 7 x )} + \frac{1}{( 6 y )} = 3

, subsitute

y

with

\frac{1}{6} : x = \frac{1}{14}

Verify solutions by plugging them into the original equations

Therefore, the final solution for

\frac{1}{( 7 x )} + \frac{1}{( 6 y )} = 3, \frac{1}{( 2 x )} - \frac{1}{( 3 y )} = 5

(x = \frac{1}{14}, y = \frac{1}{6})

5 x + 2 y = 7, 7 x + 6 y = - 3

5 x + 7 y = 3, 3 x + 14 y = 6

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

3 x + 4 y = 14, \frac{( x - y )}{2} - \frac{( 6 x + 9 y )}{10} = - 3

3 x + 4 y = 84, 5 x + 3 y = 96

What is 1/((7x))+1/((6y))=3, 1/((2x))-1/((3y))=5 ?
The solution to 1/((7x))+1/((6y))=3, 1/((2x))-1/((3y))=5 is