Chapter EP, Problem 3.3.2EP

To determine

Solve the system of inequalities by graphing.

Answer to Problem 3.3.2EP

Region 2 is the solution for the inequality $y<3$ and $y-x\ge -1$ .

Explanation of Solution

Given information:

The given equations are:

  $\begin{array}{l}y<3\\ y-x\ge -1\end{array}$

In the above graph, the solution for the inequality $y<3$ is labelled by Region 1 and Region 2. The solution for inequality $y-x\ge -1$ is labelled by Region 2 and Region 3.

Since Region 2, is part of solution for both inequalities. It is the solution of the system.

Checking:

The origin $\left(0,0\right)$ can be used as a test point, since it is the part of the solution of the system. Use this ordered pair to test the solution.

Equation: $y<3$

  $y<3$ Write the inequality

  $0<3$ Substitute the value of $y$

  $0<3$ True

Equation: $y-x\ge -1$

  $y-x\ge -1$ Write the inequality

  $\begin{array}{l}0-0\ge -1\\ 0\ge -1\end{array}$ Substitute the value of $y$

  $0\ge -1$ True