To solve the given system of linear equations by graphing, we can analyze the two equations:
- \(y = 5x + 3\)
- \(y = 5x + 15\)
Both equations are in slope-intercept form \(y = mx + b\), where \(m\) is the slope and \(b\) is the y-intercept.
For both equations:
- The slope is 5, which means they are parallel lines.
- The y-intercept of the first equation is 3, and the y-intercept of the second is 15.
Since both lines have the same slope but different y-intercepts, they will never intersect. Therefore, there are no solutions to this system of equations.
The correct answer is: No solutions.