To determine how many solutions the system of equations has, we can rewrite the second equation in a more standard form and analyze the two equations:
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The first equation is already in slope-intercept form:
\[ y = 3x - 2 \]
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The second equation can be rearranged. Starting with:
\[ -3x + y = 7 \]
We can add \(3x\) to both sides to get:
\[ y = 3x + 7 \]
Now we have the two equations:
- \(y = 3x - 2\)
- \(y = 3x + 7\)
Next, we observe the slopes of both equations. Both equations have a slope of 3. Since they have the same slope but different y-intercepts (-2 and +7), this means the lines are parallel.
Since parallel lines never intersect, this system of equations has no solutions.
Therefore, the answer is 0 solutions.