Question

Solve the system by graphing:

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

Short answer

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

Step-by-step solution

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 3x-2y≥12 

We will graph $3x-2y\ge 12$by graphing $3x-2y=12$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 ≥ 32x + 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.