Question

x/3 - y/4=1 x/8 + y/3 =25/12

Answer 1

Two statements are
CASE 1.
(X / 3) - (Y / 4) = 1
LCM is 12
(4X - 3Y) / 12 = 1
4X - 3Y = 12 ............... (1)

CASE 2.
(X / 8) + (Y / 3) = 25 / 12
LCM is 24
(3X + 8Y) / 24 = 25 / 12
Reduce denominator
(3X + 8Y) / 2 = 25.
3X + 8Y = 50 ............. (2)

Multiply (1) by 3 & (2) by 4 to make X variable equal in both
[4X - 3Y) = 12] x 3
= 12X - 9Y = 36 ............... (1'')

[(3X + 8Y) = 50.] x 4
= 12X + 32Y = 200 .................. (2'')

Subtract (1'') from (2'')
(12X - 12X) + [32Y - (-9Y)] = 200 - 36
41Y = 164
Y = 164 / 41
Y = 4

Subsitute Y value in (2'') 12X + 32Y = 200
12X + (32 x 4) = 200
12X + 128 = 200
12X = 200 - 128
12X = 72
X = 72 / 12
X = 6

Therefore, the values of X = 6 & Y = 4