Hey there! I'll try to provide you with my best answer.
Answer: x = 120 and y = 150
(x / y) = (4 / 5)
1) 5x = 4y
( (x + 20 ) / (y - 20) ) = (14 / 13)
cross multiply fractions
13(x + 20) = 14(y - 20)
13x + 260 = 14y - 280
2) 13x - 14y = -540
solve equation 1) for x
x = 4y/5
now substitute for x in equation 2)
13(4y/5) - 14y = -540
multiply both sides of = by 5
52y - 70y = -2700
-18y = -2700
y = 150
x = 4(150) / 5 = 120
x = 120 and y = 150
check answers (proof):
120 / 150 = 12 / 15 = 4 / 5
(120+20) / (150-20) = 140 / 130 = 14 / 13
