Question

Use the image to answer the question.
-3x + y = 7
y = 3x - 2
The graphs represent this system:
y = 3x - 2
-3x + y = 7
How many solutions does this system have: 0, 1, or infinite?
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Answer 1

To determine how many solutions the given system of equations has, we need to analyze the equations:

1. \( y = 3x - 2 \)
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.