Question

1.) Determine whether the ordered pair is a solution of the given system.

Answer 1

In the ordered pair (2, 12), x = 2 and y = 12.
Substitute these values into each inequality to see if the resulting inequality is true. 
y > 2x + 4 
12 > 2(2) + 4    Twelve is greater than 2 times 2 plus 4 ...hmmm
12 > 4 + 4
12 > 8               Twelve is greater than 8 ....this is TRUE...go to the next inequality
y < 3x + 7
12 < 3(2) + 7    Twelve is less than 3 times 2 plus 7 ...interesting
12 < 6 + 7
12 < 13             Twelve is less than 13 ... this is TRUE also 
Therefore; the answer is b. Yes
It must create a true inequality for BOTH inequalities in order for the ordered pair to be a solution

Answer 2

Just put X,Y in the ordered pair into the equation and evaluate.  
Then do the same with the second equation and evaluate.
When you do this the answer would be b. Yes