Write a system of linear inequalities represented by the graph. 20 pts!

Question

asked Dec 14, 2022 224k views

1 Answer

Druckermann · Answer 1 · 2022-12-18T14:33:18+0000

Given:

The graph of the system of inequalities.

To find:

The system of inequalities.

Solution:

From the given graph it is clear that the first line passes through the points (0,2) and (1,-1). So, the equation of the boundary line is:

y-y_1=(y_2-y_1)/(x_2-x_1)(x-x_1)

y-2=(-1-2)/(1-0)(x-0)

y-2=-3x

y=-3x+2

The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.

$y\geq -3x+2$

The second line passes through the points (0,-2) and (3,0). So, the equation of the boundary line is:

y-(-2)=(0-(-2))/(3-0)(x-0)

y+2=(2)/(3)x

y=(2)/(3)x-2

The shaded region lies above the line and the boundary line is a solid line. So, the sign of inequality must by ≥.

$y\geq (2)/(3)x-2$

Therefore, the system of inequalities contains two linear inequalities
$y\geq -3x+2$ and
$y\geq (2)/(3)x-2$ .