Question

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

y < −2x + 10
y < 1 over 2x − 2

1. I
2. B
3. A
4. F

Answer 1

Option 4. 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 slope of the dashed line A is negative m=-2

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

The x-intercept of the dashed line A 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 slope of the dashed line B is positive m=1/2

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

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

The solution of the system of inequalities is the shaded area below the dashed line A and below the dashed line B

Remember that

If a point is a solution of the system of inequalities, then the point is in the shaded area of the solution set of the system

using a graphing point

Graph the solution of the system of inequalities

see the attached figure

The solutions point are

E,J,F and G

The point H is not a solution because the line B is a dashed line