Question

Which system of equations is indicated by this description?

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:
\[
{x + 3 = 2y, \; 5y = -x - 10}
\]