Three students are working to find the solution set of this system of equations: y = 2x + 6 2y = 4x – 2 Use the drop-down menus to complete the statements about each of their methods. Shannon Shannon correctly graphs the two lines and sees that they ____. This means the system has ____. David David correctly sees that y ____ be equal to both 6 more than twice a number and 1 less than twice a number at the same time. Alex Alex correctly concludes that because 2x + 6 and 2x – 1 will ____ be equal, the system has ____.

Let’s analyze the system of equations step by step:

1. Equations Given:

– ( y = 2x + 6 )

– ( 2y = 4x – 2 )

We can simplify the second equation by dividing all terms by 2, giving us:

– ( y = 2x – 1 )

2. Finding Intersection Points:

To find the solution set, we can set the two equations for (y) equal to each other:

( 2x + 6 = 2x – 1 )

3. Solving the equation:

Subtract (2x) from both sides:

( 6 = -1 )

This leads us to a contradiction, which indicates that there is no solution to the system.

Now, let’s fill in the statements for each student:

Shannon

Shannon correctly graphs the two lines and sees that they are parallel. This means the system has no solution.

David

David correctly sees that (y) cannot be equal to both 6 more than twice a number and 1 less than twice a number at the same time.

Alex

Alex correctly concludes that because (2x + 6) and (2x – 1) will never be equal, the system has no solution.

In