Question

The graph of a system of inequalities is shown.

Answer 1

Answer:

The system is

$x+2y \leq -8$

$y> 2x$

Step-by-step explanation:

Part 1

Find the equation of the first inequality

we know that

The first line is a solid line with negative slope passing through the points (-6,-1) and (0,-4)

The slope is equal to

$m=(-4+1)/(0+6)\\m=-0.5$

The equation of the solid line in slope intercept form is

$y=-0.5x-4$

Everything below the line is shaded

so

The inequality is

$y \leq -0.5x-4$

Convert to standard form

Adds 0.5x both sides

$0.5x+y \leq -4$

Multiply by 2 both sides

$x+2y \leq -8$ -----> First inequality

Part 2

Find the equation of the second inequality

we know that

The second line is a dashed line with positive slope passing through the points (-2,-4) and (0,0)

This line represent a proportional relationship, because the line passes through the origin

The slope is equal to the constant of proportionality

$k=(-4)/(-2)=2$

The equation of the dashed line is

$y=2x$

Everything to the left of the line is shade

so

The inequality is

$y> 2x$ -----> Second inequality

see the attached figure to better understand the problem

Answer 2

Answer:

the correct anwser is A.......

     y > 2x

x + 2y ≤ –8               just took the  unit test

Step-by-step explanation: