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 correctly graphs the two lines and sees that they ______. This means the system has ______. 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 correctly concludes that because 2x + 6 and 2x – 1 ______ be equal, the system has ______.

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

1. We begin with the equations:

– Equation 1: ( y = 2x + 6 )

– Equation 2: ( 2y = 4x – 2 )

2. For David’s observation, if both equations are evaluated at the same point, that point should satisfy both equations simultaneously. David correctly sees that ( y ) cannot be equal to both results from the two different expressions.

3. For Shannon’s statement, if she graphs both lines and sees that they cross at a single point, this means the system is consistent and has one unique solution.

4. Alex’s statement about ( 2x + 6 ) and ( 2x – 1 ) can be incorporated to reveal that since these two expressions yield different outputs for any x-value, the system does not have any points that satisfy both equations simultaneously.

Now, filling in the statements based on the above analysis:

– Shannon correctly graphs the two lines and sees that they intersect at one point. This means the system has one unique solution.

– 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 correctly concludes that because ( 2x + 6 ) and ( 2x – 1 ) cannot be equal, the system has **