Rewrite the equation 3x+y=7

Question

3
x
+
y
=
7
in slope-intercept form to select the statement that correctly describes the system of equations

Statement #1: The system of equations has no solutions because the graphs of the two equations are parallel lines.

Statement #2: The system of equations has an infinite number of solutions because the graphs of the two equations occupy the same line.

(2 points)
The equation 3x+y=7
3
x
+
y
=
7
is y=
y
=

in slope intercept form, which means that statement #
describes the system of equations.

Answer 1

To rewrite the equation \(3x + y = 7\) in slope-intercept form \(y = mx + b\), we can isolate \(y\):

\[ y = -3x + 7 \]

Now we can analyze the two statements regarding the system of equations.

Since you have mentioned only one equation, there isn't a second equation provided.

• Statement #1 implies that there is another equation with the same slope as this equation \(y = -3x + 7\) that results in parallel lines, which means they would not intersect and would have no solutions.
• Statement #2 implies that there is another equation that is exactly the same as this one, meaning that the two lines are the same, resulting in infinitely many solutions.

Given that we cannot assess the truth of either statement without a second equation, we can only confirm the result for the one provided.

Thus, you should fill in the answer as such:

The equation \(3x + y = 7\) is \(y = -3x + 7\) in slope-intercept form, which means that statement #1 or #2 describes the system of equations depending on the second equation that is not provided. If the second equation has the same slope and intercept, statement #2 would be accurate. If the second equation has the same slope but a different intercept, statement #1 would be accurate.