Determine which system below will produce infinitely many solutions.
−6x + 3y = 18
4x − 3y = 6

2x + 4y = 24
6x + 12y = 36

3x − y = 14
−9x + 3y = −42

5x + 2y = 13
−x + 4y = −6

Question

Determine which system below will produce infinitely many solutions.
−6x + 3y = 18
4x − 3y = 6

2x + 4y = 24
6x + 12y = 36

3x − y = 14
−9x + 3y = −42

5x + 2y = 13
−x + 4y = −6

anonymous · Answer

Please help me

welshfella · Answer

infinitely many solutions occur  when one equation is a multiple of the other. Basically they produce they produce the same line in the coordinate plane.

anonymous · Answer

Okay.. so what would I do to find the answer?

welshfella · Answer

an example would be
  x + y = 6
-2x - 2y = -12

- because the second equation = first  multiplied by -2

welshfella · Answer

see if you can find something similar  in the 4 given options
are the y , x terms and the number in one equation multiplied by the same value to get the other?

anonymous · Answer

Oh okay, I'll look back at them and see. Thank you so much !!

welshfella · Answer

yw

Hint - at first it looks like number 2 is the one  because 2x* 3 = 6x and 4y * 3 = 12y

but 24 *3  does not equal 36 so its not that one.

anonymous · Answer

Yeahh true ... hm. Algebra is my hardest so I dont really know what to do exactly

welshfella · Answer

look at number 3 how do you go from 3x   to -9x,  and -y to 3y and  14 to -42?

anonymous · Answer

It multiplies by 3 ?

anonymous · Answer

-3*

welshfella · Answer

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