The sum of two number is 63the smaller number is 17 less than the larger number. what are the number

x=40
y=23.

Explanation:
Let x be equal to the larger number.
Let y be equal to the smaller number.

Using the given information, we can come up with the following equations:

x+y=63
x-y=17

From here, we can use the method of elimination to find the value of x by adding the equations together. Please check the image attached!

2x=80
Divide both sides by 2 to isolate x
2x/2=80/2
x=40

Now, we can substitute x back into one of our original equations to solve for y.

x-y=17
40-y=17
Subtract both sides by 40 to isolate y
-y=17-40
-y=-23
y=23

Therefore, x=40 and y=23.

I hope this helps! Please comment if you have any questions :)