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anonymous
 one year ago
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 =1/4xa
c) Let c represent a Real Number.
2x + 6y = 4c
3x + 9y = 6c
anonymous
 one year ago
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 =1/4xa c) Let c represent a Real Number. 2x + 6y = 4c 3x + 9y = 6c

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anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i need some help please

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I 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
 one year ago
Best ResponseYou've already chosen the best response.0One 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=2xk. These are two lines with the same slope, 2. But they have different yintercepts. So, they are parallel and never intersect. For b, these two lines have to intersect in one point, since they have different slopes and yintercepts. Part c is like part a. They are two parallel lines, so there are no solutions.

radar
 one year ago
Best ResponseYou've already chosen the best response.0Note that C. The second equation is simply the first equation times 1 1/2. Does that give you any ideas?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0My mistake, in part c they are parallel lines (same slope) with the same yintercept. 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
 one year ago
Best ResponseYou've already chosen the best response.0sorry for late reply@ Titanic12

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we can pick a # for them but then how can i know how many solutions they have

radar
 one year ago
Best ResponseYou've already chosen the best response.0Titantic12 is correct just reread 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.
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