How do I check if this answer is really correct in elimination method.
1.) 3x - 2y = 6              SS={(4,3)}
    5x + 7y = 41

Substitute (4) for x  and (3) for y in both equations to see if 
you end up with a true equation:

 3(4) - 2(3) = 6      5(4) + 7(3) = 41
      12 - 6 = 6          20 + 21 = 41
           6 = 6               41 = 41

It is true both that 6 = 6 and that 41 = 41. Therefore (4,3) is a solution
and {(4,3)} is the solution set.


2.) 5x - 2y = 8              SS={(2,1)}
    3x - 5y = 1

Substitute (2) for x and (1) for y in both equations to see if 
you end up with a true equation:

5(2) - 2(1) = 8       3(2) - 5(1) = 1
     10 - 2 = 8             6 - 5 = 1
          8 = 8                 1 = 1

It is true both that 8 = 8 and that 1 = 1. Therefore (2,1) is a solution
and {(2,1)} is the solution set.

[If either had turned out to be false like if instead of 8 = 8 it was 8 = 9
1 = 2 or or something else that's false, then that would not be the solution.
But in both problems here what were given as their solution set were correct.

Edwin