Question

Which graph represents the solution set of the system of inequalities?

{y≥12x+1y>−x−2



A

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma negative 2 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.

B

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 4 comma 3 end ordered pair. The region above the solid line and above the dashed line is shaded.

C

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 2 comma negative 4 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region below the solid line and above the dashed line is shaded.

D

A system of 2 linear inequalities graphed on a coordinate plane. The horizontal x axis ranges from negative 5 to 5 in increments of 1. The vertical y axis ranges from negative 5 to 5 in increments of 1. A dashed line passes through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 1 comma negative 1 end ordered pair and begin ordered pair 0 comma 1 end ordered pair. The region above the solid line and above the dashed line is shaded.

Answer 1

Option A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 4 comma 3 end ordered pair. The region above the solid line and above the dashed line is shaded

Explanation:

we have

`y\geq 1/2x+1` ----->inequality A

`y > -x-2` ----> inequality B

we know that

The solution of the inequality A is the shaded area above the solid line
`y=1/2x+1`

The slope of the solid line is positive

The y-intercept of the solid line is the point (0,1)

The x-intercept of the solid line is the point (-2,0)

The solution of the inequality B is the shaded area above the dashed line
`y > -x-2`

The slope of the dashed line is negative

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

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

The solution of the system of inequalities is the shaded area between the solid line and the dashed line

see the attached figure

Option A dashed line passes through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair negative 5 comma 3 end ordered pair. A solid line passing through begin ordered pair negative 2 comma 0 end ordered pair and begin ordered pair 4 comma 3 end ordered pair. The region above the solid line and above the dashed line is shaded