please help me guy :))
In each of the following systems of equations, look at the system and determine whether it
has infinitely many solutions, no solution, or one solution. Explain in each case how you
came to your conclusion. You should not attempt to solve any of the systems.
a) Let k represent a Real Number.
y = 2x + k
y = 2x − k
b) Let a represent a Real Number.
y = −4x + a
y =1/4x-a
c) Let c represent a Real Number.
2x + 6y = 4c
3x + 9y = 6c

Question

please help me guy :))
In each of the following systems of equations, look at the system and determine whether it
has infinitely many solutions, no solution, or one solution. Explain in each case how you
came to your conclusion. You should not attempt to solve any of the systems.
a) Let k represent a Real Number.
y = 2x + k
y = 2x − k
b) Let a represent a Real Number.
y = −4x + a
y =1/4x-a
c) Let c represent a Real Number.
2x + 6y = 4c
3x + 9y = 6c

anonymous · Answer

i need some help please

anonymous · Answer

I wonder why they say "don't solve the systems." The best way I can think of is to pick a number for k, a, and c, and then try different xs.

anonymous · Answer

One way to think about it is this:
For part a, the coordinate pairs satisfying the first equation are (x,y) such that y=2x+k, while the points satisfying the second equation are (x,y) such that y=2x-k. These are two lines with the same slope, 2. But they have different y-intercepts. So, they are parallel and never intersect.

For b, these two lines have to intersect in one point, since they have different slopes and y-intercepts.

Part c is like part a. They are two parallel lines, so there are no solutions.

radar · Answer

Note that C.  The second equation is simply the first equation times 1 1/2.  Does that give you any ideas?

anonymous · Answer

My mistake, in part c they are parallel lines (same slope) with the same y-intercept. So there would be infinitely many solutions. You can also look at it like Radar said: the second of the two equations is just the first multiplied by a constant factor. Thus the coordinate pairs on that line will be the same as those on the first line.

anonymous · Answer

sorry for late reply@ Titanic12

anonymous · Answer

@radar

anonymous · Answer

we can pick a # for them but then how can i know how many solutions they have

radar · Answer

Titantic12 is correct just re-read his post (fifth post above this one.  Please note the second sentence.  

A big lot plus some more is close enough to infinite, they don't expect you to keep trying values till you reach an infinite number, because you won't.