Question

Rewrite the equation 3x+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
is y=

in slope intercept form, which means that statement #
describes the system of equations.
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Answer 1

To rewrite the equation \(3x + y = 7\) in slope-intercept form (which is \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept), we can solve for \(y\):

1. Start with the original equation:
\[
3x + y = 7
\]

2. Isolate \(y\) by subtracting \(3x\) from both sides:
\[
y = -3x + 7
\]

Now we have the equation in slope-intercept form:
\[
y = -3x + 7
\]

In this form, we can see that the slope \(m\) is \(-3\) and the y-intercept \(b\) is \(7\).

Regarding the statements:

- **Statement #1:** If the other equation has the same slope of \(-3\) and a different y-intercept, then the system has no solutions because the graphs are parallel lines.
- **Statement #2:** If the other equation is exactly the same (i.e., \(3x + y = 7\) or \(y = -3x + 7\)), then the system has an infinite number of solutions because they are the same line.

Since I do not have the specific second equation to analyze, here's how you fill in the blanks:

The equation \(3x + y = 7\) is \(y = -3x + 7\).

Depending on the second equation, select:

- If the second equation has the same slope but a different y-intercept, choose **Statement #1**.
- If the second equation is identical to the first, choose **Statement #2**.