Question 971828
Choose any number.
 Add 10 to the number.
 Multiply the result by 2.
 Subtract 18 from the result.
 Multiply the result by one half. (dividing by two is the same)
 Subtract the original number.
y = {{{(2(x+10)-18)/2}}} - x
:
To find the number a person would have chosen to obtain a final result of 1, solve the linear system consisting of the equation you wrote and the equation 
:
y = {{{(2(x+10)-18)/2}}} - x
Multiply by 2,cancel the denominator and you have 
2y = 2(x + 10) -  18 - 2x 
2y = 2x + 20 - 18 - 2x
2y = 2x - 2x + 2
2y = 2
y = 1
:
You can see it is 1 no matter what x equals