We have two formulas:
(4/7)x - (1/2)y = 5
x-y=1
So, let's do some substituting. Let's replace y with x-1:
(4/7)x - (1/2)(x-1) = 5
Expand out a bit:
(4/7)x - (1/2)x + 1/2 = 5
(4/7-1/2)x + 1/2 = 5
Multiply the lot by 2 to make it nicer:
(8/7-1)x + 1 = 10
(1/7)x=9
x = 9×7 = 63
and so y = 62
Check: (4/7)63 - (1/2)62 = 36 - 31 = 5
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