SOLUTION: The graph of the system y=2x+2 6x-3y=-6 consists of two lines that: a. intersect at one point b. do not intersect c. are not in the same place d. intersect in an infinite nu

Algebra ->  Coordinate Systems and Linear Equations  -> Lessons -> SOLUTION: The graph of the system y=2x+2 6x-3y=-6 consists of two lines that: a. intersect at one point b. do not intersect c. are not in the same place d. intersect in an infinite nu      Log On


   

Question 572390: The graph of the system
y=2x+2
6x-3y=-6
consists of two lines that:
a. intersect at one point
b. do not intersect
c. are not in the same place
d. intersect in an infinite number of points
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
y=2x%2B2 is the equation of a line in slope-intercept form. The slope is the 2 multiplying the x, and the y-intercept is the +2 at the end.
If the two lines do not have the same slope, they intersect at one point. If the slopes are the same they lines could be parallel (do not intersect) or the same line (intersect at all points).
The beauty of the slope-intercept form is that there is only one slope-intercept form for each line.
6x-3y=-6 is in a different form, and they can trick you with all the other forms, because there are many ways to represent the same line.
The equation can be transformed into the slope intercept form by solving for y
6x-3y=-6 --> 6x-3y%2B6=-6%2B6 --> 6x-3y%2B6=0 --> 6x-3y%2B6%2B3y=3y --> 6x%2B6=3y --> %281%2F3%29%286x%2B6%29=%281%2F3%29%283y%29 --> 2x%2B2=y or y=2x%2B2
It turns out that both equations represent the same line. Their graph is the same line. The "two lines" are the same line and all the infinite same points belong to the "two lines" , so the answer is d.