To rewrite the equation \(3x + y = 7\) in slope-intercept form (\(y = mx + b\)), we need to solve for \(y\).
Starting with the original equation:
\[ 3x + y = 7 \]
Subtract \(3x\) from both sides:
\[ y = -3x + 7 \]
Now, in slope-intercept form, the equation is:
\[ y = -3x + 7 \]
This tells us that the slope (\(m\)) is \(-3\) and the y-intercept (\(b\)) is \(7\).
Now, you need a second equation to analyze the system of equations. Assuming you have a second equation, you would compare the slopes:
- If the slopes are different, the system has one solution (the lines intersect).
- If the slopes are the same but the y-intercepts are different, the system has no solutions (the lines are parallel).
- If the slopes and y-intercepts are the same, the system has infinitely many solutions (the lines are the same).
Since you only provided one equation, we can't definitively choose Statement #1 or Statement #2 without additional context regarding the second equation.
However, based on the transformed equation \(y = -3x + 7\):
- If the second line is not parallel (has a different slope or is the same line), we cannot confirm either statement.
In conclusion:
The equation \(3x + y = 7\) is \(y = -3x + 7\) in slope-intercept form, which means that without additional information about a second equation, we cannot select either statement with certainty.
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