How to determine the variables x,y,z if y+z-x=8 and 5x=4y, x/4=z/7?

We'll recall the fact that the number of variables to be
determined has to be equal to the number of relations
provided.

We notice that we have to determine 3 variables
and the problems gives us three conditions, therefore the variables can be
determined.

We'll express the y and z terms with respect to
x.

5x = 4y <=> y =
5x/4

x/4 = z/7 <=> z =
7x/4

We'll replace y and z into the relation y+z-x = 8,
such as:

5x/4 + 7x/4 - x = 8 <=> 12x/4 - x =
8

3x - x = 8

2x = 8 =>
x = 4

We'll determine y and
z:

x = 4 => y = 5*4/4 => y =
5

x = 4 => z = 7*4/4 => z =
7

The variables x , y  and z are: x=4 , y=5 ,
z=7.