Explain.
Numbers may only be used once 1-9

Step-by-step explanation:

Ax − B = C

Dy + E = F

Solve for x and y:

x = (B + C) / A

y = (F − E) / D

So the sum of x and y is:

x + y = (B + C) / A + (F − E) / D

For x + y to be as large as possible, A, E and D must be small, and B, C, and F must be large.  With some trial and error:

x + y = (9 + 8) / 1 + (7 − 3) / 2

x + y = 17 + 2

x + y = 19

For x + y to be as small as possible, we want the first term to be a small fraction, and the second term to be as negative as possible.  So A must be large, B + C must be small, F must be less than E, and D must be small.

x + y = (3 + 4) / 8 + (2 − 9) / 1

x + y = ⅞ − 7

x + y = -6⅛