Question

The coordinate grid shows points A through K. What point is a solution to the system of inequalities?

y > -2x + 10

y > 1/2x - 2

Choices:

E

K

B

D ​

Answer 1

Answer:

Option C, i.e., point B.

Step-by-step explanation:

The given system of inequalities is

$y>-2x+10$     ...(1)

$y>\dfrac{1}{2}x-2$     ...(2)

If a point is a solution of given system of inequalities, then the both inequalities must be satisfy by the point.  

From the given graph it is clear that coordinates of point E are (4,-2).

Put x=4 and y=-2 in (1).

$-2>-2(4)+10\Rightarrow -2>2$ False.

From the given graph it is clear that coordinates of point K are (2,3).

Put x=2 and y=3 in (1).

$3>-2(2)+10\Rightarrow 3>6$ False.

From the given graph it is clear that coordinates of point B are (4,7).

Put x=4 and y=7 in (1).

$7>-2(4)+10\Rightarrow 7>2$ True.

Put x=4 and y=7 in (2).

$7>\dfrac{1}{2}(4)-2\Rightarrow 7>0$ True.

Since both inequalities are true for B(4,7), therefore point B is the solution.

From the given graph it is clear that coordinates of point D are (-7,1).

Put x=-7 and y=1 in (1).

$1>-2(-7)+10\Rightarrow 1>24$ False.

Since the given inequalities are false for points E, K and D, therefore they are not the solution.