Answer:
Explanation:
i.
(10y+x) - (10x+y) = 63 ---> This subtracts the original from the number with the reversed digits, and makes it equal to 63, so the number increases by 63
y - x = 7 ---> We have to prove this is true, so put it into the original equation
y = 7 + x ---> manipulate the above equation, and substitute it into the original equation
[10 (7 + x) + x] - [10x + (7 + x)] = 63
(70 + 11x) - (11x + 7) = 63
63 = 63 ---> Solve the equation, and because it comes out to be true, you proved that y - x = 7
ii. a.
(10x + y) + (10y + x) = 99 ---> The sum of the original and reversed numbers
x + y = 9
y = 9 - x ---> substitute this into the original equation
[10x + (9 - x)] + [10 (9 - x) + x] = 99
(9x + 9) + (90 - 9x) = 99
99 = 99
ii. b.
infinitely many solutions