I how to solve this in elimination. If it's no solution or infinitely many solutions I'm absolutely confused

Question

-3x—2y=6

3x+2y=0

 

Answer 1

Add the two equations together:

 

-3x - 2y = 6

 3x + 2y = 0

-------------

  0  + 0  =  6

 

0 = 6

 

No solutions (aka, inconsistent).  If you convert the two equations to slope-intercept form, you get y = -(3/2)x-3 and y = (-3/2)x.  These are two parallel lines, same slope (= -3/2) but different y-intercepts (-3 vs. 0).  Parallel lines never cross, so there is no solution.

 

 

Answer 2

-3x - 2y = 6

 3x + 2y = 0       Add the two equations.

 

0 + 0 = 6            Impossible.

 

No solution.