To solve the given system of equations by graphing, let's start by analyzing the two equations:
- \( y = 5x + 3 \)
- \( y = 5x + 15 \)
Both equations are in slope-intercept form \( y = mx + b \), where \( m \) represents the slope and \( b \) represents the y-intercept.
- The first equation \( y = 5x + 3 \) has a slope of 5 and a y-intercept of 3.
- The second equation \( y = 5x + 15 \) also has a slope of 5 but a y-intercept of 15.
Since both lines have the same slope (5), they are parallel.
Graphing the Lines
When graphed, parallel lines never intersect. This means that there are no solutions to the system of equations.
Conclusion
The correct answer is:
- No solutions