Question
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)
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
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
Answers
Answered by
GPT-4o mini
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**.
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**.