Answer:
Option D.
Step-by-step explanation:
The given system of inequalities are
\(4x+y>3\)
\(x-y>2\)
We need to find a solution for the following system of inequalities.
Check each point by these inequalities.
For (-2,-2)
\(4(-2)+(-2)>3\Rightarrow -10>3\) False
So, (-2,-2) is not included in the solution set.
For (1,-5)
\(4(1)+(-5)>3\Rightarrow -1>3\) False
So, (1,-5) is not included in the solution set.
For (0,0)
\(4(0)+(0)>3\Rightarrow 0>3\) False
So, (0,0) is not included in the solution set.
For (5,-2)
\(4(5)+(-2)>3\Rightarrow 18>3\) True
\((5)-(-2)>2\Rightarrow 7>2\) True
Both inequalities are true for the point (5,-2). So, the point (5,-2) is a solution for the following system of inequalities
Therefore, the correct option is D.
