Two numbers have a sum of 10 . if you add the first number to twice the second number, the result is 8. what are the numbers.

Let's call the first number "x" and the second number "y". From the problem, we know two things:

1. x + y = 10 (the sum of the two numbers is 10)
2. x + 2y = 8 (if you add the first number to twice the second number, the result is 8)

We can use algebra to solve for x and y. Here's one way to do it:

1. Solve the first equation for x: x = 10 - y
2. Substitute x in the second equation with 10 - y: 10 - y + 2y = 8
3. Simplify the equation: 10 + y = 8
4. Solve for y: y = -2
5. Use the value of y to solve for x using the first equation: x + (-2) = 10, so x = 12

Therefore, the two numbers are 12 and -2.

Note: It's always a good idea to check your answer to make sure it makes sense in the context of the problem. In this case, we can see that 12 + (-2) does indeed equal 10, and that 12 + 2(-2) equals 8. So we can be confident that our solution is correct.