Question

Two numbers have a sum of 23 and a difference of 9 find the 2 numbers

Answer 1

Define a variable for the unknown numbers.

`\text{ let the numbers be x and y}`

The sum is 23, implies

`x+y=23`

The difference is 9 is written as

`x-y=9`

Then we have the system of equation

`\begin{gathered} x+y=23\ldots\text{equation}1 \\ x-y=9\ldots\text{equation}2 \end{gathered}`

Add equation 1 and 2.

`\begin{gathered} 2x-0=32 \\ 2x=32 \end{gathered}`

Divide both sides by 2

`\begin{gathered} (2x)/(2)=(32)/(2) \\ \text{Then} \\ x=16 \end{gathered}`

hence x=16

Recall equation 1

`\begin{gathered} x+y=23 \\ \text{ put x=16} \\ 16+y=23 \end{gathered}`

Subtract 16 from both sides, we have

`\begin{gathered} 16-16+y=23-16 \\ y=7 \end{gathered}`

Hence, y=7

Answer: The numbers are 16 and 7