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

Question

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.

The equation 3x + y = 7 is 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, we solve for \(y\):

\[ y = -3x + 7 \]

Now we can compare the two equations:

1. The first equation in slope-intercept form is \(y = -3x + 7\).
2. The second equation is already given as \(y = -3x + 7\).

Since both equations are identical, they represent the same line.

Now we can analyze the provided statements:

• Statement #1: The system of equations has no solutions because the graphs of the two equations are parallel lines. (This is incorrect because the lines are not parallel; they are the same line.)

• Statement #2: The system of equations has an infinite number of solutions because the graphs of the two equations occupy the same line. (This is correct because both equations represent the same line.)

Thus, the completed response is:

The equation \(3x + y = 7\) is \(y = -3x + 7\) in slope-intercept form, which means that statement #2 describes the system of equations.