To determine how many solutions the given system of equations has, we need to analyze the equations:
- \( y = 3x - 2 \)
- \( -3x + y = 7 \) (which can be rewritten as \( y = 3x + 7 \))
Next, we will compare the slopes and y-intercepts of both equations:
- The first equation \( y = 3x - 2 \) has a slope of 3 and a y-intercept of -2.
- The second equation, when rewritten, \( y = 3x + 7 \), also has a slope of 3, but a different y-intercept of 7.
Since both lines have the same slope (3), they are parallel to each other. Because the y-intercepts are different (-2 and +7), these lines will never intersect.
Thus, the system of equations has:
0 solutions.
The lines are parallel and will never meet.