Plug (x,y) = (1,19) into the first inequality
y <= 7*x - 13
19 <= 7*1 - 13
19 <= 7 - 13
19 <= -6
The inequality is false. The number 19 is not smaller than -6, nor is it equal. So the point (1,19) is NOT a solution to the system of inequalities
We don't need to check the other inequality, but let's do so just for the sake of completeness
y > 3*x + 6
19 > 3*1 + 6
19 > 3 + 6
19 > 9
this inequality is true, but again it doesn't matter since the first one is not true
Overall, the point (1,19) is not in the solution set