Question

are there any number pairs that satisfy both constrians the sum is 12 and the difference is 5. is my answer correct

Answer 1

The two numbers are 3.5 and 8.5

Explanation:

To find the missing numbers, create a system of equations that satisfies:

1. The sum is 12:

`x+y=12`

2. The difference is 5:

`x-y=5`

Isolate one of the variables in equation 2 and plug it into equation 1:

`x=5+y`

Plugging it into equation 1:

`\begin{gathered} (5+y)+y=12 \\ 2y+5=12 \\ 2y=12-5 \\ y=(7)/(2) \\ y=3.5 \end{gathered}`

Now, if y=7/2 satisfies, substitute it into equation 2:

`\begin{gathered} x=5+(7)/(2) \\ x=(17)/(2) \\ x=8.5 \end{gathered}`