Solve the following system of linear equations by graphing. Choose the answer that matches the solution.

To solve the system of linear equations by graphing, we need to analyze the two equations:

1. \( y = 5x + 3 \)
2. \( y = 5x + 15 \)

Both equations are in slope-intercept form (y = mx + b), where the slope (m) is 5 for both lines. However, the y-intercepts (b) are different:

• The first line has a y-intercept of 3.
• The second line has a y-intercept of 15.

This means that both lines have the same slope but different y-intercepts, indicating that they are parallel lines.

When graphing, parallel lines will never intersect. Therefore, there are no points (x, y) that satisfy both equations simultaneously.

Thus, the correct answer is:

No solutions

Yes, I am sure. Let's revisit the setup step by step to reinforce the conclusion:

1. Identifying the equations:

   • Equation 1: \( y = 5x + 3 \) (this line has a slope of 5 and a y-intercept of 3)
   • Equation 2: \( y = 5x + 15 \) (this line also has a slope of 5 but a different y-intercept of 15)

2. Understanding the slopes:

   • Both lines have the same slope (5), which means they rise at the same angle.

3. Understanding the intercepts:

   • The difference in y-intercepts (3 and 15) indicates that the two lines are parallel, meaning they will never cross or intersect at any point.

4. Conclusion:

   • Since the lines are parallel, there is no solution that satisfies both equations simultaneously.

The final conclusion remains that there are No solutions to this system of equations, as they represent two distinct parallel lines in a graph.