The difference of two numbers is equal to 4. The sum of three times one of the numbers and the other number is equal to 34. Which system represents this situation? (1 point) Responses x×y=4 and 3x+3y=34 x×y=4 and 3x+3y=34 x−y=4 and 3x+y=34 x−y=4 and 3x+y=34 x÷y=4 and 3x+y=34

Answer 1

Let's denote the two numbers as \( x \) and \( y \).

From the problem, we have two conditions:

1. The difference of the two numbers is equal to 4, which can be expressed as: \[ x - y = 4 \]

2. The sum of three times one of the numbers and the other number is equal to 34. Assuming we take three times \( x \) and add \( y \), this can be expressed as: \[ 3x + y = 34 \]

So the system of equations that represents this situation is:

1. \( x - y = 4 \)
2. \( 3x + y = 34 \)

From the provided options, the correct choice is: \[ x - y = 4 \text{ and } 3x + y = 34 \]

(Note that it appears that there is a repetition in your options: "x−y=4 and 3x+y=34" appears twice in the choices.)