What is 3y-x=3, 2/((3y))-1/x =2 ?

The solution to 3y-x=3, 2/((3y))-1/x =2 is

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3y-x=3, 2/((3y))-1/x =2

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

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

Solution steps

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

Isolate

y

for

3 y - x = 3 : y = \frac{3 + x}{3}

Plug the solutions

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

into

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

For

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

, subsitute

y

with

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

Plug the solutions

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

into

3 y - x = 3

For

3 y - x = 3

, subsitute

x

with

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

For

3 y - x = 3

, subsitute

x

with

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

Verify solutions by plugging them into the original equations

Therefore, the final solutions for

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

are

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

3 x + y = 11, 2 x y = 5

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

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

d (ab) a = 4, b = 7

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