Which system of equations is indicated by this description?

Question

x increased by 3 is equal to the product of 2 and y.
5 times y is equal to negative x minus 10.
(1 point)
Responses

{x+3=2y5y=x−10
- no response given

{3x=2y5y=−x−10
- no response given

{x+3=2+y5y=−x−10
- incorrect

{x+3=2y5y=−x−10
no response given
Incorrect

The term product indicates "multiplication," not addition.
Remaining Attempts : 1

Answer 1

To create the system of equations based on the given description, we can break it down as follows:

1. "x increased by 3 is equal to the product of 2 and y." This can be translated into the equation: \[ x + 3 = 2y \]

2. "5 times y is equal to negative x minus 10." This can be translated into the equation: \[ 5y = -x - 10 \]

So the system of equations represented would be: \[ \begin{cases} x + 3 = 2y \ 5y = -x - 10 \end{cases} \]

Based on the responses provided, the correct system seems to be represented as:

\({x + 3 = 2y, , 5y = -x - 10 }\)

Let's confirm the right structure:

• First equation: \(x + 3 = 2y\).
• Second equation: \(5y = -x - 10\).

Final Answer:

The correct system of equations is: \[ {x + 3 = 2y, ; 5y = -x - 10} \]