Questions: Find the value of two numbers if their sum is 12 and their difference is 4. Let x be the first number, and y be the second. Set up a system of equations, then solve for x and y.

Solution Steps

We are given two conditions:

1. The sum of the two numbers is 12:
   \[ x + y = 12 \]
2. The difference of the two numbers is 4:
   \[ x - y = 4 \]

Add the two equations to eliminate \( y \): \[ (x + y) + (x - y) = 12 + 4 \] \[ 2x = 16 \] \[ x = 8 \]

Substitute \( x = 8 \) into the first equation to solve for \( y \): \[ 8 + y = 12 \] \[ y = 4 \]

Final Answer