Question

2x+y< 1

y≥1/2x+2

What graph represents the system of linear inequalities?

picture 1,2,3 or 4

Answer 1

It's the second option/image

It's figure 2

Answer 2

The graph in the attached figure

Explanation:

we have

`2x+y < 1` ----> inequality A

The solution of the inequality A is the shaded area below the dashed line
`2x+y=1`

The slope of the dashed line is negative m=-2

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

The x-intercept of the dashed line is (0.5,0)

`y\geq (1)/(2)x+2` ----> inequality B

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

The slope of the solid line is positive m=1/2

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

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

using a graphing tool

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

The graph in the attached figure