Question

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

Answer 1

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:

$y-y_1=\dfrac{y_2-y_1}{x_2-x_1}(x-x_1)$

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

$y-2=-3x$

$y=-3x+2$

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:

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

$y+2=\dfrac{2}{3}x$

$y=\dfrac{2}{3}x-2$

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

$y\geq \dfrac{2}{3}x-2$

Therefore, the system of inequalities contains two linear inequalities $y\geq -3x+2$ and $y\geq \dfrac{2}{3}x-2$.