Question

40 POINTS!!!!!!!!! Given the following system of equations and their graph below, what can be determined about the slopes and y-intercepts of the system of equations? A line includes points 6 comma 1 and 4 comma 0. 3x − 6y = 12 9x − 18y = 36 The slopes are different, and the y-intercepts are different. The slopes are different, and the y-intercepts are the same. The slopes are the same, and the y-intercepts are different. The slopes are the same, and the y-intercepts are the same.

Answer 1

The slopes are the same and the y-intercepts are the same.

Explanation:

Answer 2

The slopes are the same and the y-intercepts are the same.

Explanation:

Looking at the two systems of equations:

3x - 6y = 12

and

9x - 18y = 36

We can see that the two equations have a GCF, that GCF would be 3.

Since, 3 ( 3x - 6y = 12) = 9x - 18y = 36

or vice versa: (9x - 18y = 36)/3 = 3x - 6y = 12

Therefore, both the slopes and the y-intercepts are the same just dilated by a factor of 3.