Remember that ordered pairs are written in the form (x,y).
Then, to check if (-2,4) is a solution to the system of inequalities, both of the given inequalities should be verified when replacing x=-2 and y=4.
Replace x=-2 and y=4 into the inequalities and check if both of them are satisfied or not.
-3x > -7y - 3
Sice 6 is greater than -31, then this inequality is satisfied by (-2,4).
7x > -5y-4
Since -14 is greater than -24, then this inequality is satisfied by (-2,4).
Since both inequalities are satisfied by (-2,4) then (-2,4) is a solution to the given system of inequalities.