To analyze the given system of equations:
- First Equation: \( y = 2x + 1 \)
- Second Equation: \( y = 2x + 13 \)
Both equations are in the slope-intercept form \( y = mx + b \), where \( m \) is the slope and \( b \) is the y-intercept.
- Slope: Both equations have the same slope of \( 2 \).
- Y-Intercept: The first equation has a y-intercept of \( 1 \), and the second equation has a y-intercept of \( 13 \).
Since they both have the same slope (2) but different y-intercepts (1 and 13), this means the lines are parallel. Therefore, they will never intersect, indicating that there are no solutions to the system of equations.
The correct response is:
Both equations have a slope of 2, but they do not share the same y-intercept. Thus, the system has no solutions because the lines are parallel.