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 linear equations by graphing, let's analyze the given 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, but the y-intercepts are different (3 and 15).

Since both lines have the same slope but different y-intercepts, they are parallel and will never intersect. This means there are no solutions to this system.

Therefore, the correct response is:

No solutions.