3x+y=4 -6x-2y=12

This is because these 2 lines are paralle.

they have the same gradient

I can tell straight off that they are parallel because

-6x-2y=-2(3x+y)

The -2 is not important.  It is important that one is a constant multiple of the other.

This is a system of equations:

 

3x + y = 4

-6x - 2y = 12

 

Note, we can multiply the first equation by 2 and then add the two equations together!

 

2(3x + y) = 2(4)

-6x - 2y = 12

 

    6x + 2y = 8

+ -6x - 2y = 12

_________________

0 = 20.

0 cannot equal 20.

 

There is no solution!