Answer: Only (-6,10) is a solution. The other points are not.
Explanation
The idea is to plug the x and y coordinates into the inequality. Then simplify. If we arrive at a true statement, then that (x,y) point is a solution.
Let's try (x,y) = (-10,-7). Meaning x = -10 and y = -7 pair up together.
x+y > 2
-10+(-7) > 2
-17 > 2
The last inequality is false, so the first inequality is also false for that x,y pair of values. The point (-10,-7) is not a solution. Other non-solution points are:
In contrast, the point (-6,10) is a solution point because of this scratch work.
x+y > 2
-6+10 > 2
4 > 2
The last inequality is true, so the first inequality is true for that x,y pair.
This confirms that (-6,10) is a solution
Notice the graph below. The point (-6,10) is in the blue shaded region. The other points are not. Points on the dashed boundary are not part of the solution set. If we wanted to include the boundary then we'd need "or equal to" in the inequality sign.
