Question

I will award you! :)

Which system will have an infinite number of solutions?

A. -4y=-6x+8
y=3/2x-2

B. -4x+5y=8
5y=-4x+6

C. -2x+4y=3
y=1/2x+6

D. 2x-6y=9
5y=-4x+6

Answer 1

@SolomonZelman :)

Answer 2

The system has an infinite solutions, if 2 equations are multiples of each other.

Lets work out choice A.
\(\normalsize\color{blue}{ -4y=-6x+8 }\)
\(\normalsize\color{blue}{ y=3/2x-2 }\) multiply this equation times `-4`, and you get

\(\normalsize\color{blue}{ -4y=-6x+8 }\)

Answer 3

Tell me if you need more help.

Answer 4

i need more help, haha. These are really confusing to me. :/

Answer 5

Okay, so do you see that in option A, if you multiply the second equation times `-4` you will then get the same thing as the first equation ?

Answer 6

yeah.

Answer 7

That means that this system has infinitely many solutions.

Answer 8

I just don't get why you multiply it by -4

Answer 9

You multiply by -4 so you have the same coefficient on the y variables

Answer 10

Another method would have been to divide the first equation by -4 to get both equations equal to y. If they are the same equation then they have infinitely many solutions.

Answer 11

I wish i could give you guys both medals! :p

Answer 12

http://www.algebra.com/algebra/homework/Equations.faq.question.158249.html
This may help explain what is going on.