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


A) I
B) B
C) A
D) F

Answer 1

Option D) F

Explanation:

we have

`y < -2x+10` -----> inequality A

The solution of the inequality A is the shaded area below the dashed line
`y=-2x+10`

The y-intercept of the dashed line is (0,10)

The x-intercept of the dashed line is (5,0)

`y < (1)/(2)x-2` ----> inequality B

The solution of the inequality B is the shaded area below the dashed line
`y=(1)/(2)x-2`

The y-intercept of the dashed line is (0,-2)

The x-intercept of the dashed line is (4,0)

The solution of the system of inequalities is the shaded area between the two dashed lines

see that attached figure

Remember that

If a ordered pair is a solution of the system of inequalities, then the ordered pair must lie on the shaded area of the solution

therefore

The solution are the points

E, F and G