Whether an ordered pair is a solution to a system of equations can be determined by substituting the x and y values of this pair into the given system of equations.
So, let us check for the ordered pair (2, -1).
For the first equation:
Substitute x = 2 and y = -1 into 5x+3y=7,
5*2 + 3*(-1) = 10 - 3 = 7
Hence, (2, -1) satisfies the first equation.
Now, let's check the second equation:
Substitute x = 2 and y = -1 into 6x-2y=15,
6*2 - 2*(-1) = 12 + 2 = 14
We see that (2, -1), does not satisfy the second equation since 14 is not equal to 15.
Therefore, the ordered pair (2, -1) is not a solution of the system {5x+3y=7, 6x-2y=15} because it doesn't satisfy both equations simultaneously.