Question 469870: How do I check if this answer is really correct in elimination method.
1.) 3x - 2y = 6 SS={(4,3)}
5x + 7y = 41
2.) 5x - 2y = 8 SS={(2,1)}
3x - 5y = 1
Answer by Edwin McCravy(20056)   (Show Source):
You can put this solution on YOUR website!
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
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