he Number Machine starts with two numbers, one represented by X$,$ the other represented by Y$,$ and has a big red button on it$.$ Each time the button is pressed, the Machine first adds $3$ to X$,$ and secondly subtracts the new value of X from Y$.$ This can also be shown in this way:

Step $1$: X$=$ X $+3$

Step $2$: Y $=$ Y$-$ X

The starting value for X is $2,$ and the starting value for Y is $45.$ If the button is pressed three times, what is the sum of X and Y at the end?