let x represent gallons of $19 paint
let y represent gallons of $3 paint
first you make your 2 equations
x+y=16, y=16-x
(19x+3y) ÷ 16 = 14
then you use substitution
14 = (19x + 3(16-x) ) ÷16
224 = 19x + 48 - 3x
176 = 16x
11 = x, so there's 11 gallons of $19 paint
recall that x+y=16
11+y=16
5=y
so there are 11 gallons of $19 paint and 5 gallons of $3 paint