xy + 4x= 2880 → x (y + 4) = 2880 → x = 2880/ (y + 4) (1)
xy - 12y= 2160 (2)
Sub (1) into (2)
[2880/ (y + 4)] y - 12y = 2160 multiply through by ( y + 4)
2880y - 12y( y + 4) = 2160( y + 4) simplify
2880y - 12y^2 - 48y = 2160y + 8640
12y^2 - 672 y + 8640 = 0
y^2 - 56y + 720 = 0 factor
( y - 36) (y - 20) = 0
Set each factor to 0 and y = 36 or y = 20
When y = 36, x = 2880/[36 + 4] = 2880/40 = 72
When y = 20, x = 2880/[20 + 4] = 2880/24 = 120
Solutions (72, 36) and (120, 20 )