Question

PLEASE HELP!!!

A system of linear inequalities is graphed below.

What are the linear inequalities for the system? Show your work, or explain your answer.

Answer 1

System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0

Explanation:

Given:

• The dotted line has two points as (-1,0) and (0,1).

• The solid line also has two points as (-6,0) and (0,-3).

To Find:

• Linear inequality for the system.

Formula used:

• Equation of a line passing through point (x1, y1) and (x2, y2) is given by
• (y-y1) = (y2-y1)/(x2-x1) * (x-x1)

According to question, we have

Inequality for dotted line :

(y-1) > (0-1)/(-1-0) * (x-0)

y - 1 > x

x - y + 1 < 0...(1)

Inequality for solid line:

(y-(-3)) < (0-(-3))/(-6-0) * (x-0)

y + 3 < -x/2

x + 2y +6 < 0...(2)

Using (1) and (2), we get

System of linear inequalities is x - y + 1 < 0 and x + 2y +6 < 0.