To solve this system of equations, we can start by solving the first equation for x in terms of y and z.

2/3x = 3/4y
Multiply both sides by 3/2 to isolate x:
x = (3/4y)(3/2)
x = 9/8y

Now we can substitute this expression for x into the second equation:

(9/8y) + y - z = 57
Multiply both sides by 8 to eliminate the fraction:
9y + 8y - 8z = 456
17y - 8z = 456

Now let's solve the first equation for z in terms of x and y:

2/3x = 4/5z
Multiply both sides by 5/4 to isolate z:
z = (4/5z)(5/4)
z = 2/3x

Substitute this expression for z into the equation 17y - 8z = 456:

17y - 8(2/3x) = 456
17y - 16/3x = 456
Multiply both sides by 3 to eliminate the fraction:
51y - 16x = 1368

Now we have two equations:

17y - 8z = 456
51y - 16x = 1368

We can solve this system of equations using substitution or elimination method.