To rewrite the equation \( 3x + y = 7 \) in slope-intercept form (which is \( y = mx + b \)), we need to isolate \( y \):
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Start with the original equation: \[ 3x + y = 7 \]
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Subtract \( 3x \) from both sides: \[ y = -3x + 7 \]
Now, we have the equation in slope-intercept form: \[ y = -3x + 7 \]
Analyzing the Statements
If you are comparing this equation to another linear equation and trying to determine if they are parallel or the same line, you'll need to look at the slopes:
- The slope \( m \) of this equation is \( -3 \).
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.
Since we currently have only one equation, we cannot conclude the relationship with any other equation without additional information. However, here's how you could fill in your answer based on the provided text:
The equation \( 3x + y = 7 \) is \[ y = -3x + 7 \] in slope-intercept form, which means that statement #1 describes the system of equations (assuming you have another equation with a parallel slope).
If the other equation has a different slope, you would choose Statement #1; if it has the same slope and y-intercept, you would choose Statement #2 instead.
In conclusion: The equation \( 3x+y=7 \) is \( y = -3x + 7 \) in slope-intercept form, which means that statement #1 describes the system of equations if comparing against a different line with a slope of -3, otherwise more context is needed.
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