The difference of two numbers is -6 The sum of twice one of the numbers and the other number is 78, Which system represents this situation?(1 point)

Question

Responses

x×y=−6 and 2x+2y=78x×y=−6 and 2x+2y=78

x÷y=−6 and 2x+y=78x÷y=−6 and 2x+y=78

x−y=−6 and 2x+y=78

Answer 1

To translate the given information into a system of equations, let's define the two numbers as \( x \) and \( y \).

1. The difference of the two numbers is -6, which can be represented as: \[ x - y = -6 \]

2. The sum of twice one of the numbers and the other number is 78 can be represented as: \[ 2x + y = 78 \]

Putting this together, the system of equations is: \[ x - y = -6 \quad \text{and} \quad 2x + y = 78 \]

The correct response is: x - y = -6 and 2x + y = 78.