Question

Which system of linear inequalities is represented by the graph?

Answer 1

Answer:

The system of linear inequalities which is represented by the  graph is:

        y>x-2 and    y<x+1

Step-by-step explanation:

The first inequality--

It is a dotted line which passes through (-1,0) and (0,1) and the shaded region is below the line.

first we find the equation of line:

The equation of a line passing through (a,b) and (c,d) is given by:

$y-b=\dfrac{d-b}{c-a}\times (x-a)$

Hence,

(a,b)=(-1,0) and (c,d)=(0,1)

Hence, the equation of line is:

$y-0=\dfrac{1-0}{0-(-1)}\times (x-(-1))\\\\i.e.\\\\y=\dfrac{1}{1}\times (x+1)\\\\i.e.\\\\y=x+1$

Also, the inequality is strict since the line is dotted.

Hence, the inequality is given by: y<x+1

The second inequality --

is a dotted line which passes through (0,-2) and (2,0)

and the shaded region is above the line.

The equation of line is given by:

  y=x-2

and the inequality is strict.

Hence, the inequality is given by:

        y>x-2

Answer 2

I can’t see it clearly but so far the answer is D. Hope this helps!