Question

a word problem states: \the sum of two numbers is 12. one number is 4 more than the other.\ which system of equations represents this situation?
options:

1. ( \begin{cases} x + y = 12 \\ x = y + 4 end{cases} )
2. ( \begin{cases} x + y = 4 \\ x = y + 12 end{cases} )
3. ( \begin{cases} x - y = 12 \\ x = y + 4 end{cases} )
4. ( \begin{cases} x + y = 12 \\ y = 4x end{cases} )

Explanation:

Step1: Analyze the sum condition

The sum of two numbers (let's say \(x\) and \(y\)) is 12, so the equation should be \(x + y=12\).

Step2: Analyze the "4 more" condition

One number is 4 more than the other. If we assume \(x\) is 4 more than \(y\), then \(x=y + 4\).

Step3: Match with the options

Looking at the options, the first option has the system \(

$$\begin{cases}x + y=12\\x=y + 4\end{cases}$$

\), which matches our derived equations. The second option has \(x + y = 4\) which is incorrect. The third option has \(x-y=12\) which is incorrect. The fourth option has \(y = 4x\) which is incorrect.

Answer:

The first option (with \(x + y = 12\) and \(x = y + 4\))