Answer:
The correct option is D.
Step-by-step explanation:
The given inequality is
[tex]y\leq 2x-2[/tex]
[tex]y\leq x^2-3x[/tex]
Any point is a solution of this system of inequality if it satisfy both inequalities.
Check the inequalities by each option.
For (-2,-1),
[tex]-1\leq 2(-2)-2\Rightarrow -1\leq -6[/tex]
This statement is false, because -1 is greater than -6. Therefore (-2,-1) is not a solution and option A is incorrect.
For (1,3),
[tex]3\leq 2(1)-2\Rightarrow 3\leq 0[/tex]
This statement is false, because 3 is greater than 0. Therefore (1,3) is not a solution and option B is incorrect.
For (2,1),
[tex]1\leq 2(2)-2\Rightarrow 1\leq 2[/tex]
[tex]1\leq (2)^2-3(2)\Rightarrow 1\leq -2[/tex]
This statement is false, because 1 is greater than -2. Therefore (2,1) is not a solution and option C is incorrect.
For (4,2),
[tex]2\leq 2(4)-2\Rightarrow 2\leq 6[/tex]
[tex]2\leq (4)^2-3(4)\Rightarrow 2\leq 4[/tex]
Both statements are true. Therefore (4,2) is a solution and option D is correct.