The sum of two numbers is 17, and their difference is 29. What are the two numbers?

X + y = 17

x - y = 29

x = 17 - y

x - y = 29

x = 17 - y

17 - y - y = 29

x = 17 - y

17 - 2y = 29

x = 17 - y

- 2y = 29 - 17

x = 17 - y

-2y = 12

x = 17 - y

y = - 6

x = 17 - (-6)

y = - 6

x = 17 + 6

y = - 6

x = 23

y = - 6

X + y = 17

x - y = 29

We're going to do substitution.

1. We first put one of these in terms of x or y. Either are fine, but I'm going to do x, and any of the equations are fine, but I'm going to do the first one.

x + y = 17 >> x = - y + 17

2. We plug in this x-value into the other equation, and solve for the variable.

(-y+17) - y = 29

-2y + 17 = 29

-2y = 12

y = - 6

3. We now plug the variable we found (y in this case) into the first equation to find the other variable (x).

x + - 6 = 17 >> x = 23

In conclusion, the two numbers are 23 and - 6.