Chapter EP, Problem 3.3.4EP

To determine

Solve the system of inequalities by graphing.

Answer to Problem 3.3.4EP

Region 2 is the solution for the inequality $y+x<2$ and $y\ge x$ .

Explanation of Solution

Given information:

The given equations are:

  $\begin{array}{l}y+x<2\\ y\ge x\end{array}$

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

  $y+x<2$ Write the inequality

  $\begin{array}{l}0+0<2\\ 0<2\end{array}$ Substitute the value of $x$ and $y$

  $0<2$ True

Equation: $y\ge x$

  $y\ge x$ Write the inequality

  $0\ge 0$ Substitute the value of $x$ and $y$

  $0\ge 0$ True