Question

Solve 7x-4y=8?

Answer 1

As this is an equation with two variables there are an infinite number of possible solutions.

Explanation:

for example x = 1 y = -1/4

or x = 0 y = -2

Answer 2

See below

Explanation:

We can consider equation above as a Diofantic equation `Ax-By=C`

A diofantic equation is a particular case of general equation where solutions are allways integers

We consider by now the homogeneus case

`7x-4y=0`. The general solution of this equation is `x=4t` and `y=7t` with `t` an integer parameter (infinite solutions)

Now the complete case solutions are obtained

`x=x_0+4t`
`y=y_0+7t`

where `x_0, y_0` are paticular solutions of homegeneus case

The solution is unique if and only if GCD(A,B) divide to C