Question

Determine which system below will produce infinitely many solutions.
Choices:
-4x + 6y = 20 and 4x - 3y = -2

-2x + 4y = 18 and 4x - 8y = -36

3x - 2y = 5 and -6x - 4y = -10

5x - 3y = 12 and 15x - 9y = 24

Answer 1

which one is just a multiple of the other?

Answer 2

what do you mean?

Answer 3

i mean, given ax + by = c, which one shows the other equation for some multiple n:

an x + bn y = cn

Answer 4

for example:

5x - 3y = 12
15x - 9y = 24

is one a multiple of the other? is there some value n, that we can mutliply by that will turn one into the other?

5x - 3y = 12
*3 *3 *3
15x - 9y = 24
^^ this doesnt work 12*3 = 36

Answer 5

Oh okay so you just do that to find out which is one multiple of the other and which ever one is that's the answer?

Answer 6

another trick is to divide one by the other and see if they all form the same value

lets try #1, stack them one over the other and divide the numbers

-4x + 6y = 20
4x - 3y = -2
--------------
-1 -2 -10

these arent all the same so its not this one either

Answer 7

yes, which ever one fits the bill isthe solutions

Answer 8

dividing using the first example:

15x - 9y = 24
5x - 3y = 12
-------------
3 3 2 notice we still get a bad result and therefore its
not this one still

Answer 9

Alright I think I got what you meant on how to do this :) thank you.

Answer 10

youre welcome :)