so the value of the number is 8 times the sum of its digits:
10x-y=8(x+y)
how can we show that the numbers digits are reversed using our variables? the numbers digits being reversed means that the digit that was in the tens place is now in the ones place and vise versa. so the reversed digit number would look like this: 10y+x
(10x+y)-45=10y+x
now you can solve the system of equations.
10x+y=8(x+y)
solve for one variable, i’ll choose x
2x=7y
x=7/2y, or 3.5y
(10x+y) - 45= 10y+x
go to your second equation
(10•3.5y+y)-45=10y+3.5y
plug in for x
36y-45=45
y=2
x=3.5y go back to the equation where you solved for c in terms of y
x=3.5(2)
plug in for y
x=7
the number is 72
let’s check
1. 72=8(7+2)
72=8(9)
72=72
2. 72-45= 27
27=27