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
