Answer:
The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.
![rank(A)=rank\left ( \left [ A|B \right ] \right )\:and\:n=rank(A)](https://tex.z-dn.net/?f=rank%28A%29%3Drank%5Cleft%20%28%20%5Cleft%20%5B%20A%7CB%20%5Cright%20%5D%20%5Cright%20%29%5C%3Aand%5C%3An%3Drank%28A%29)
Then satisfying this theorem the system is consistent and has one single solution.
Explanation:
1) To answer that, you should have to know The Rouché-Capelli Theorem. This theorem establishes a connection between how a linear system behaves and the ranks of its coefficient matrix (A) and its counterpart the augmented matrix.
![rank(A)=rank\left ( \left [ A|B \right ] \right )\:and\:n=rank(A)](https://tex.z-dn.net/?f=rank%28A%29%3Drank%5Cleft%20%28%20%5Cleft%20%5B%20A%7CB%20%5Cright%20%5D%20%5Cright%20%29%5C%3Aand%5C%3An%3Drank%28A%29)

Then the system is consistent and has a unique solution.
<em>E.g.</em>

2) Writing it as Linear system


3) The Rank (A) is 3 found through Gauss elimination


4) The rank of (A|B) is also equal to 3, found through Gauss elimination:
So this linear system is consistent and has a unique solution.
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Answer:
Its most likely the last one
Explanation:
But like, what kind of quesiton is this?
5x+2y=3
Slope = -5.000/2.000 = -2.500
x-intercept = 3/5 = 0.60000
y-intercept = 3/2 = 1.50000
2x+3y=13
Slope = -1.333/2.000 = -0.667
x-intercept = 13/2 = 6.50000
y-intercept = 13/3 = 4.33333