Question

Please help asap

Write the system of linear inequalities that would produce the following graph
Thank you in advance

Answer 1

The system of inequalities are

x - y < 1 and y < - 2

Explanation:

The horizontal line shown in the graph has equation y = - 2 {As it is parallel to x-axis}

Now, this line is dotted and the lower portion of the graph is shaded.

So, the inequality will be y < - 2 ......... (1)

Again, another line is there in the graph which passes through the points (1,0) and (0,-1)

So, its equation will be
`(y + 1)/(- 1 - 0) = (x - 0)/(0 - 1)`

⇒ y + 1 = x

⇒ x - y = 1

Now, the origin (0,0) is within shaded zone of the inequality and putting x = 0 and y = 0, we get

0 - 0 < 1

So, the equation of the inequality is x - y < 1 {As the line is dotted}

Therefore, the system of inequalities are

x - y < 1 and y < - 2 (Answer)