Fan and medal!

Determine which system below will produce infinitely many solutions.

2x + 5y = 24
2x + 5y = 42

3x - 2y = 15
6x + 5y = 11

4x - 3y = 9
-8x + 6y = -18

5x - 3y = 16
-2x + 3y = -7

Question

Fan and medal!

Determine which system below will produce infinitely many solutions.

 2x + 5y = 24
2x + 5y = 42

 3x - 2y = 15
6x + 5y = 11

 4x - 3y = 9
-8x + 6y = -18

 5x - 3y = 16
-2x + 3y = -7

gorv · Answer

3rd one both the equation are same 
just first one multiplied by -2

gorv · Answer

so it will produce infinite solution

anonymous · Answer

Thanks :)

gorv · Answer

4x - 3y = 9
4x=9+3y
x=(9+3y)/4
put it in other equation 
-8((9+3y)/4) + 6 y= -18
-2(9+3y)+6y=-18
-18-6y+6y=-18
0=0
it does not depend on value of x or y so we can take any value that is infinite solution