Q. 4.112 - Intermediate Algebra

Question

Solve the system by graphing

$\left\{\begin{array}{l}x > -4\\ x - 2y \ge -4.\end{array}\right.$

Step-by-Step Solution

Answer

The solution of the system of inequalities $\left\{\begin{array}{l}x > -4\\ x - 2y \ge -4.\end{array}\right.$ is a common region of the inequalities represented by the dark region by the graph given below:

Step 1. Given information

The given system of inequalities are: 

$\left\{\begin{array}{l}x > -4\\ x - 2y \ge -4.\end{array}\right.$

Step 2. Graph the inequality x > - 4

We will graph $x>-4$ by graphing $x=-4$ and the boundary will be a solid line because it contains greater than sign.

The graph is given as:

Step 2. graph the inequality x - 2 y ≥ - 4

We will graph the inequality by graphing $x-2y=4$ on the same graph and the boundary line will be solid since it contains greater than equal to sign.

The graph is given as:

The solution of the given system of inequalities is the common region between inequalities represented by the dark region (dark blue) in the above graph. 

Step 4. Check the solution

Substitute the ordered pair $\left(5,0\right)$ in both equalities as it is in the solution region.

For inequality $x>-4$

 $$\begin{gathered} x>-4 \\ 5>-4 \end{gathered}$$

This is true

For inequality $x-2y\ge -4$

$$\begin{gathered} 5-2\times 0>-4 \\ 5>-4 \end{gathered}$$

This is also true.

Thus, solution set is correct.