Question

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

{y≤14x−2y≥−54x+2



Coordinate graph showing a range of negative five and five on both axes. A solid line through begin ordered pair 0 comma 2 end ordered pair and begin ordered pair 4 comma negative 3 end ordered pair. Another solid line through begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair 4 comma negative 1 end ordered pair. Four regions are created by the intersection of the two lines. The right region is the shaded region.

Coordinate graph showing a range of negative five and five on both x and y axes. A solid line through begin ordered pair 0 comma 2 end ordered pair and begin ordered pair 4 comma negative 3 end ordered pair. A dashed line through begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair 4 comma negative 1 end ordered pair. Four regions are created by the intersection of the two lines. The upper right region is the shaded region.

Coordinate graph showing a range from negative seven to three on both x and y axes. A solid line through begin ordered pair 0 comma 2 end ordered pair and begin ordered pair negative 4 comma negative 3 end ordered pair. A dashed line through begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair negative 4 comma negative 3 end ordered pair. Four regions are created by the intersection of the two lines. The lower left region is the shaded region.

Coordinate graph showing a range of negative five to five on both x and y axes. A solid line through begin ordered pair 0 comma 2 end ordered pair and begin ordered pair negative 4 comma negative 3 end ordered pair. A dashed line through begin ordered pair 0 comma negative 2 end ordered pair and begin ordered pair 4 comma negative 1 end ordered pair. Four regions are created by the intersection of the two lines. The upper left region is the shaded region.

Answer 1

The right region is the shaded region.

see the attached figure

Explanation:

we have

`y\leq (1)/(4)x-2` ----> equation A

The solution of the inequality A is the shaded area below the solid line
`y=(1)/(4)x-2`

The slope of the solid line is positive

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

The x-intercept of the solid line is (8,0)

`y\geq -(5)/(4)x+2` ----> equation B

The solution of the inequality B is the shaded area above the solid line
`y=-(5)/(4)x+2`

The slope of the solid line is negative

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

The x-intercept of the solid line is (1.6,0)

using a graphing tool

Four regions are created by the intersection of the two lines

The right region is the shaded region.

see the attached figure