Write ar. ' solve a system of equations that represents (Examples 1-4) 1. The sum of two numbers is 20.5 . Their difference is 6.5 . Find the two numbers.

Let's define the two numbers as \( x \) and \( y \). Based on the information given, we can create a system of equations: 1. \( x + y = 20.5 \) (The sum of the two numbers) 2. \( x - y = 6.5 \) (The difference between the two numbers) Now, we can solve this system using the method of substitution or elimination. By adding the two equations together, we have: \[ (x + y) + (x - y) = 20.5 + 6.5 \] This simplifies to: \[ 2x = 27 \implies x = \frac{27}{2} = 13.5 \] Next, substitute \( x \) back into the first equation to find \( y \): \[ 13.5 + y = 20.5 \implies y = 20.5 - 13.5 = 7 \] Thus, the two numbers are \( x = 13.5 \) and \( y = 7 \). Ultimately, plugging in these values confirms they satisfy both original equations. So, we have successfully found the two numbers: 13.5 and 7!