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