Question

Which graph represents the following system of inequalities? y < -x - 4 y > 2x - 3

Answer 1

Answer:

Option 4 is correct.

Explanation:

We are given two inequality y<-x-4 and y>2x-3.

We need to choose correct graph from given choices.

First we draw the graph of each equation

Equation 1: y<-x-4

We draw the graph using slope intercept form.

Slope=-1 and y-intercept (0,-4)

Test point (0,0). Put (0,0) into equation 1 y<-x-4

We get $0$. This is false statement. Graph will shade away from point (0,0).

Equation 2: y<2x-3

We draw the graph using slope intercept form.

Slope=2 and y-intercept (0,-3)

Take test point (0,0). Put (0,0) into equation 2, y>2x-3

We get $0>-3$. This is true statement. Graph will shade towards the point (0,0).

Please take a look attachment for the graph.

Option 4 is correct.

Answer 2

We have that
y < -x - 4
y > 2x - 3

using a graph tool
see the attached figure
 the solution is the option D----------> see the attached figure