Question

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)

Answer 1

D. (4,2)

Explanation:

Find the point that is in the dark region

Answer 2

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.