Chapter 6, Problem 25PT

To determine

To calculate:

The solution set of following inequalities system by graphing method:

  $\begin{array}{l}y\ge 2x+3\\ -4x-3y>12\end{array}$

Answer to Problem 25PT

The shaded area is solution of given inequalities shown by the following graph:

  

Explanation of Solution

Given information:

  $\begin{array}{l}y\ge 2x+3\\ -4x-3y>12\end{array}$

Calculation:

The given system of equation is:

  $y\ge 2x+3$........(1)

  $-4x-3y>12$........(2)

Now isolate both equations as:

  $y\ge 2x+3$........(3)

And

  $\begin{array}{l}3y<-12-4x\\ y=\frac{-12-4x}{3}\end{array}$

  $y=-4-\frac{4}{3}x$........(4)

First, draw two equations (3) and (4) separately as above.

  

Then need to choose a point to estimate the side of the shaded line. So, it gives the area here the shading is available from each inequality overlap with the other one.

And the shaded area is nothing but the solution set of the given system of equations. From graph, the unbounded is observed.