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.