Question

write a system of equations in x and y describing the situation. do not solve the system. a smaller number and a larger number add up to 11 and have a difference of 1. (let x be the larger number and y be the smaller number.) choose a system of equations describing the situation. \\(\

$$\begin{cases} 2x + 2y = 11 \\\\ x - y = 1 \\end{cases}$$

\\) \\(\

$$\begin{cases} x + y = 11 \\\\ x - y = 1 \\end{cases}$$

\\) \\(\

$$\begin{cases} x + y + 11 = 0 \\\\ x - y + 1 = 0 \\end{cases}$$

\\) \\(\

$$\begin{cases} 2x = 11 \\\\ x - y = 1 \\end{cases}$$

\\)

Explanation:

Step1: Analyze the sum condition

The two numbers (x as larger, y as smaller) add up to 11, so the equation is \( x + y = 11 \).

Step2: Analyze the difference condition

The difference between the larger number (x) and the smaller number (y) is 1, so the equation is \( x - y = 1 \).

Answer:

\(

$$\begin{cases} x + y = 11 \\ x - y = 1 \end{cases}$$

\) (corresponding to the option \(

$$\begin{cases} x + y = 11 \\ x - y = 1 \end{cases}$$

\))