Question

Plz need help

graph the system of inequalities ​

Answer 1

Graph is attached. See it.

Explanation:

We have given system of inequality :

-2x + 3y >= -12

x+y < 3

We have to plot a graph of this system of inequality.

For first inequality, we plot the associated equation -2x+3y = -12

Find the x and y intercepts and join them which the solid straight line.

then put (0,0) to check the inequality.

0<= -12

It satisfy the inequality. Now shade the upper half plane.

Now draw x+y = 3 by similar procedure. Draw (0,3) and (3,0) in the graph that are they and x intercepts respectively.

Draw a dotted line joining these two points.

Testing the inequality, put (0,0) in the inequality x+y < 3 we get,

0<3.

It satisfy the inequality.

Shade the lower half plane.

The intersection of two inequalities are shown in the attached graph.

Answer 2

See graph

Explanation:

The given system of inequalities is;

`-2x+3y\ge-12`

`x+y\:<\:3`

We graph
`-2x+3y\ge-12` by graphing the corresponding equation

`-2x+3y=-12`.

We can do this by plotting the intercepts (0,-4) and (6,0).

We draw a solid line through these points.

We test the inequality with the point (0,0).

`-2(0)+3(0)\ge-12`

This is true so we shade the upper half plane.

We graph
`x+y\:<\:3` by also plotting the points (0,3) and (3,0) and draw a broken line through them.

We again test the origin

`0+0\:<\:3`

This is true, so we shade the lower half plane.

The intersection of the two region is shown in the attachment.