Question

What graph represents the system of linear inequalities? 4x+y>1 y≤32x+2

Answer 1

The graph in the attached figure

Explanation:

we have

`4x+y>1` -----> inequality A

The solution of the inequality A is the shaded area above the dashed line

The equation of the dashed line is
`4x+y=1`

The slope of the dashed line is negative

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

The x-intercept of the dashed line is the point
`(0.25,0)`

`y\leq (3)/(2)x+2` -----> inequality B

The solution of the inequality B is the shaded area below the solid line

The equation of the solid line is
`y=(3)/(2)x+2`

The slope of the solid line is positive

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

The x-intercept of the solid line is the point
`(-1.33,0)`

using a graphing tool

The graph in the attached figure