Question

Write a system of linear equations based on the verbal descriptions.

equation 1: The sum of 4 and x is equal to 17 times y.
equation 2: The difference between y and 7 is equal to the sum of 3 and x.
(1 point)
Responses

{4+x=17yy−7=3+x
enlarged left brace start layout first row 4 plus x equals 17 y second row y minus 7 equals 3 plus x end layout

{17+x=4y3y=−7x
enlarged left brace start layout first row 17 plus x equals 4 y second row 3 y equals negative 7 x end layout

{4+xy=17y−7=3x
enlarged left brace start layout first row 4 plus x y equals 17 second row y minus 7 equals 3 x end layout

{4x=17+y−7y=3x

Answer 1

To translate the verbal descriptions into a system of linear equations, we can frame them as follows:

1. For the first description: "The sum of 4 and x is equal to 17 times y."
This translates to the equation:
\( 4 + x = 17y \)

2. For the second description: "The difference between y and 7 is equal to the sum of 3 and x."
This translates to the equation:
\( y - 7 = 3 + x \)

Therefore, the system of linear equations is:

\[
\begin{aligned}
1. & \quad 4 + x = 17y \\
2. & \quad y - 7 = 3 + x
\end{aligned}
\]

Now, matching this to the potential responses, the correct one is:

**{4+x=17y, y−7=3+x}**