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

Question

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:

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