Question

What system of linear inequalities is shown in the graph?

Answer 1

Answer:  

$2y+x\geq4$

$2x-y>3$

Step-by-step explanation:

Equation of a line passes through (a,b) and (c,d) :-

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

Equation of solid line passes through (4,0) and (0,2) :-

$(y-0)=\dfrac{2-0}{0-4}(x-4)\\\\ y=\dfrac{-1}{2}(x-4)\\\\ 2y=-x+4\\\\ 2y+x=4$

Since graph is shaded above the line, so the inequality represents solid (line is included) line:  

$2y+x\geq4$

Equation of dashed line passes through (0,-3) and (1,-1) :-

$(y-(-3))=\dfrac{-1-(-3)}{1-0}(x-0)\\\\ y+3=\dfrac{-1+3}{1}(x)\\\\ y+3=2x\\\\ 2x-y=3$

Since graph is shaded above the line, so the inequality represents  dashed ( line is not included ) line:  

$2x-y>3$

Hence, the system of linear inequalities is shown in the graph :-

$2y+x\geq4$

$2x-y>3$

Answer 2

$y > 2x - 3$
$y \geqslant - \frac{1}{2}x + 2$