Question

the sum of two numbers is 12. the first number, x, is twice the second number, y. which system of equations could be used to find the two numbers?\\(\

$$\begin{cases}x + y = 12\\\\x = 2 + y\\end{cases}$$

\\)\\(\

$$\begin{cases}x + y = 12\\\\x = 2y\\end{cases}$$

\\)\\(\

$$\begin{cases}xy = 12\\\\x = 2 + y\\end{cases}$$

\\)\\(\

$$\begin{cases}xy = 12\\\\x = 2y\\end{cases}$$

\\)

Explanation:

Step1: Translate sum condition

The sum of $x$ and $y$ is 12, so:
$x + y = 12$

Step2: Translate "twice the second" condition

$x$ is twice $y$, so:
$x = 2y$

Step3: Match to options

Combine the two equations to form the system.

Answer:

$\boldsymbol{

$$\begin{cases} x + y = 12 \\ x = 2y \end{cases}$$

}$ (the second option)