Q. 4.113 - Intermediate Algebra

Question

Solve the system by graphing:

$\left\{\begin{array}{l}3x - 2y \ge 12\\ y \ge \frac{3}{2}x + 1\end{array}\right.$

Step-by-Step Solution

Answer

There is no solution to this system of inequalities as there is no common region between the inequalities in the below graph.

Step 1. Given information

The given system of inequalities are: 

$\left\{\begin{array}{l}3x - 2y \ge 12\\ y \ge \frac{3}{2}x + 1\end{array}\right.$

Step 2. Graph the inequality 3 x - 2 y ≥ 12

We will graph $3 x-2 y\ge 12$ by graphing $3 x-2 y=12$ and the boundary will be a solid line because it contains greater than equal to sign.

The graph is given as:

Step 3. graph of the inequality y   ≥   3 2 x   +   1

We will graph the inequality by graphing $y \ge \frac{3}{2}x + 1$on the same cartesian plane and the boundary line will be solid since it contains greater than equal to sign.

The graph is given as: 

There is no solution to this system of inequalities as there is no common region between the inequalities in the above graph.