# What is the Inverse of , 3x- 5y =8 Algebra 2

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Given the relation 3x- 5y =8, first determine y expressed as a function of x

3x - 5y = 8

5y = 3x - 8

y = (3x - 8)/5

Interchange x and y and isolate y again.

x = (3y - 8)/5

5x = 3y - 8

3y = 5x+8

y = (5x+8)/3

The inverse from the relation 3x- 5y =8 is y = (5x+8)/3

3x - 5y =8

To find the inverse, just interchange x and y and solve for y:

3y - 5x = 8

y = ( 5x + 8 ) / 3

The inverse is 5x + 8 / 3.

`3x- 5y =8`

`rArr 5y=3x-8`

`rArr y=(3x-8)/5=f(x)`

Now, to find the inverse interchange `x` and `y` :

`x=(3y-8)/5`

Multiply each side by 5:

`5x=3y-8`

Isolate the y term:

`3y=5x+8`

Solve for y:

`y=(5x+8)/3`

Replace` y` by `f^-1(x)` :

`f^-1(x)=(5x+8)/3`

**Therefore, the inverse of 3x- 5y =8 is** `(5x+8)/3` .

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