Determine which system below will produce infinitely many solutions.

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

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

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

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

Question

Determine which system below will produce infinitely many solutions.

-4x + 6y = 20
4x - 3y = -2 

-2x + 4y = 18
4x - 8y = -36 

3x - 2y = 5
-6x - 4y = -10 

5x - 3y = 12
15x - 9y = 24

anonymous · Answer

@SolomonZelman

campbell_st · Answer

you need to find a pair where the 2nd line is a multiple of the 1st line... 

then the lines will have a infinite number of solutions.

anonymous · Answer

I don't really get it

campbell_st · Answer

ok... so if I have 

3x - 2y = 12

and 

-12x + 8y = -48

I multiplied every term in the 1st line by -4 to get the 2nd line. 

the 1st pair are 

-4x + 6y = 20
4x - 3y = -2      

looking at the 1st line the 4x has been multiplied by -1 to get -4x in the 2nd line

applying this rule, then 20y should become -20y in the 2nd line... but its -3y

so these 2 lines are different... and will intersect.... 

hope that makes sense