Question

the sum of two numbers is 28. the first number, x, is three times the second number, y. which system of equations can be used to find the two numbers? \\(\bigcirc\\ \

$$\begin{cases} x + y = 28 \\\\ x = 3 + y \\end{cases}$$

\\) \\(\bigcirc\\ \

$$\begin{cases} xy = 28 \\\\ x = 3y \\end{cases}$$

\\) \\(\bigcirc\\ \

$$\begin{cases} xy = 28 \\\\ x = 3 + y \\end{cases}$$

\\) \\(\bigcirc\\ \

$$\begin{cases} x + y = 28 \\\\ x = 3y \\end{cases}$$

\\)

Explanation:

Step1: Translate sum condition

The sum of $x$ and $y$ is 28, so:
$x + y = 28$

Step2: Translate multiple condition

$x$ is 3 times $y$, so:
$x = 3y$

Step3: Match to options

Combine the two equations to form the system.

Answer:

$\boldsymbol{

$$\begin{cases} x+y=28 \\ x=3y \end{cases}$$

}$ (the fourth option)