Select the point that is a solution to the system of inequalities y≤2x-2 y≤x^2-3x A. (-2,-1) B. (1,3) C. (2,1) D. (4,2)

Question

asked Jul 11, 2019 13.3k views

2 Answers

Leo Antunes · Answer 1 · 2019-07-17T04:04:49+0000

Answer:

The correct option is D.

Explanation:

The given inequality is

$y\leq 2x-2$

$y\leq x^2-3x$

Any point is a solution of this system of inequality if it satisfy both inequalities.

Check the inequalities by each option.

For (-2,-1),

$-1\leq 2(-2)-2\Rightarrow -1\leq -6$

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),

$3\leq 2(1)-2\Rightarrow 3\leq 0$

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),

$1\leq 2(2)-2\Rightarrow 1\leq 2$

$1\leq (2)^2-3(2)\Rightarrow 1\leq -2$

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),

$2\leq 2(4)-2\Rightarrow 2\leq 6$

$2\leq (4)^2-3(4)\Rightarrow 2\leq 4$

Both statements are true. Therefore (4,2) is a solution and option D is correct.