Question

Which of the following systems of Inequalities would produce the region indicated on the graph below?

Answer 1

the line rising to the right has equation y = x + 2
and the  other one has equation y =  -x + 4

the lines are solid so the inequalities will be <= or >=

in both case  the shading is below so the sign is <=

also x and Y values are both positive  
so the answer is choice  C

Answer 2

The systems of Inequalities produce the region indicated on the graph below is : $y\leq -x+4,y\leq x+2,y\geq 0,x\geq 0$

We have the endpoints of the line as (4,0), (0,4)

So, the line rising to the right has equation y = x + 2

And the points of the other line are (4,6), (0,2)

So, the other one has equation y =  -x + 4

 In both case the shading is below.

So, the sign will be $\leq$

Also we see that both the values of  x and Y are positive. That is $x\geq 0,y\geq 0$

The equations that satisfies the graph is : $y\leq -x+4,y\leq x+2,y\geq 0,x\geq 0$

Therefore, the correct option is C.

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