Question

Find the value of x and y if 10x + y= 2xy-9.

Answer 1

There is no unique solution. This is just the equation of an hyperbola. Some integer solutions are

(-3,3)
(0,-9)
(1,19)
(4,7)

y = (10x+9)/(2x-1)

Answer 2

10x + y= 2xy-9
y - 2xy = -9 - 10x
y(1 - 2x) = -9-10x
y = (-9 - 10x)/(1 - 2x) or
y = ( 9+10x)/(2x-1)

pick any x you want, evaluate the y.
You can get as many values of x and y as you want.
The only value of x you can't choose is x = 1/2 , since for that value you would be dividing by zero.

e.g. let x = 1
y = (9+10(1))/(2(1) - 1)
= 19/1
= 19
so when x = 1, y = 19 or the ordered pair (1, 19)

etc.