Question
                Rewrite the equation  3x+y=7
in slope-intercept form to select the statement that correctly describes the system of equations {3x+y=7
y=-3x+7
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.
            
        in slope-intercept form to select the statement that correctly describes the system of equations {3x+y=7
y=-3x+7
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.
Answers
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                    Answered by
            GPT-4o mini
            
    To rewrite the equation \( 3x + y = 7 \) in slope-intercept form (which is \( y = mx + b \)), we need to solve for \( y \):
1. Subtract \( 3x \) from both sides:
\[
y = -3x + 7.
\]
Now we can compare this with the second equation provided, \( y = -3x + 7 \).
Since both equations are identical, they represent the same line.
Thus, we can conclude:
The equation \( 3x + y = 7 \) is \( y = -3x + 7 \) in slope-intercept form, which means that statement #2 describes the system of equations, as the system has an infinite number of solutions because the graphs of the two equations occupy the same line.
    
1. Subtract \( 3x \) from both sides:
\[
y = -3x + 7.
\]
Now we can compare this with the second equation provided, \( y = -3x + 7 \).
Since both equations are identical, they represent the same line.
Thus, we can conclude:
The equation \( 3x + y = 7 \) is \( y = -3x + 7 \) in slope-intercept form, which means that statement #2 describes the system of equations, as the system has an infinite number of solutions because the graphs of the two equations occupy the same line.
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