Question

.
Determine the number of solutions in this system.

y = 3x + 7
y = 3x - 5


(1 point)
Responses

This System has no solution because the slopes are the same and the y-intercept is different.
This System has no solution because the slopes are the same and the y-intercept is different.

This System has one solution because the slopes are different.
This System has one solution because the slopes are different.

This System has infinite solutions because the line is the same.
This System has infinite solutions because the line is the same.

This System has one solution because the y-intercepts are the same.

Answer 1

To determine the number of solutions in the given system:

1. **Identify the equations**:
- First equation: \( y = 3x + 7 \)
- Second equation: \( y = 3x - 5 \)

2. **Compare the slopes**:
- The slope of the first equation is \( 3 \).
- The slope of the second equation is also \( 3 \).

Since both slopes are the same, the lines are parallel.

3. **Compare the y-intercepts**:
- The y-intercept of the first equation is \( 7 \).
- The y-intercept of the second equation is \( -5 \).

Since the y-intercepts are different, this confirms that the lines do not intersect.

### Conclusion:
This system has **no solution** because the slopes are the same and the y-intercepts are different.

The correct response is:
**This System has no solution because the slopes are the same and the y-intercept is different.**