Question

Please Help Write a system of linear Inequalities to represent each graph.

Answer 1

Answer:

$\left\{\begin{array}{l}5x-y-7\le 0\\2x+3y-9\ge 0\end{array}\right.$

Step-by-step explanation:

1. Blue region. The boundary blue line passes through the points (0,-7) and (3,8), then its equation is

$\dfrac{x-0}{3-0}=\dfrac{y+7}{8+7},\\ \\15x=3(y+7),\\ \\5x=y+7,\\ \\5x-y-7=0.$

This line is solid, so the sign for the inequality should be with the notion "or equal to".

From the diagram you can see that the origin belongs to the blue region, then its coordinates satisfy the inequality. Thus,

$5x-y-7\le 0.$

2. Green region. The boundary green line passes through the points (6,-1) and (0,3), then its equation is

$\dfrac{x-0}{6-0}=\dfrac{y-3}{-1-3},\\ \\-4x=6(y-3),\\ \\-2x=3y-9,\\ \\2x+3y-9=0.$

This line is solid, so the sign for the inequality also should be with the notion "or equal to".

From the diagram you can see that the origin doesn't belong to the blue region, then its coordinates satisfy the inequality. Thus,

$2x+3y-9\ge 0.$

3. The system of linear inequalities that represents these graphs is

$\left\{\begin{array}{l}5x-y-7\le 0\\2x+3y-9\ge 0\end{array}\right.$