Solve the following system of linear equations by graphing. Use your Desmos calculator to graph them, and choose the answer that matches the solution.

Question

y = 5x + 3

y = 5x + 15

(1 point)
Responses

No solutions
No solutions

(3,5)
(3,5)

(5,3)
(5,3)

Infinite solutions

Answer 1

To solve the system of 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 \( m \) is the slope and \( b \) is 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.

Graphing Analysis:

1. Both lines have the same slope (5), which means they are parallel.
2. Since they have different y-intercepts (3 and 15), the lines will never intersect.

Conclusion:

With the two lines being parallel, there are no points of intersection.

Final Answer:

No solutions.