Question

I'm not getting this whole special system of equations thing. Please help me understand
Question: Which system has an infinite number of solutions? A: y = 2x - 5 and - 2 = y - 2x. B: x + 2 = y and 4 = 2y - x. C: y + 3 = 2x and 4x = 2y - x. D: 2y + 6 = 4x and - 3 = y - 2x.

Answer 1

If one equation is a multiple of the other equation, then both equations are the same, thus having infinite solutions.

Answer 2

What do you mean by multiple?

Answer 3

What I mean is, there exists a set of equations such that one of them has been multiplied by a number to disguise the fact that both of them are equal.

Answer 4

Also, terms have been switched around to disguise it even further.

Answer 5

For example, I can take

y = 2x + 3

If I multiply that by 3 I get

3y = 6x + 9

Answer 6

I can switch terms around to get

-9 = 6x - 3y

Answer 7

But no matter how much I manipulate this equation, each line is equivalent to the previous one.

Answer 8

So find the system where such a condition exists.