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)
{
4x = 17 + y
−7y = 3x
{
17 + x = 4y
3y = −7x
{
4 + x = 17y
y − 7 = 3 + x
{
4 + xy = 17
y − 7 = 3x

Answer 1

To represent the verbal descriptions as a system of linear equations, let's break down the two statements:

1. "The sum of 4 and x is equal to 17 times y."
This can be written mathematically as:
\[
4 + x = 17y
\]

2. "The difference between y and 7 is equal to the sum of 3 and x."
This can be formulated as:
\[
y - 7 = 3 + x
\]

Thus, the system of linear equations is:
\[
\begin{cases}
4 + x = 17y \\
y - 7 = 3 + x
\end{cases}
\]

Among the options provided, this corresponds to the first option:

\[
\{ 4 + x = 17y, \; y - 7 = 3 + x \}
\]