Chapter 6.6, Problem 7PPE

To determine

To find: whether the ordered pair $(2,12)$ is a solution of the given system or not.

Answer to Problem 7PPE

The ordered pair $(2,12)$ is a solution of the given system.

Explanation of Solution

Given information:

The given system is

  $\begin{array}{l}y>2x+4\\ y<3x+7\end{array}$

Calculation:

Verify the solution

Consider the inequality $y>2x+4$

  $\begin{array}{l}(2,12)\\ \Rightarrow 12>2(2)+4\\ 12>4+4\\ 12>8\text{ true}\end{array}$

Consider the inequality $y<3x+7$

  $\begin{array}{l}\Rightarrow 12<3(2)+7\\ 12<6+7\\ 12<13\text{ true}\end{array}$

Hence, the ordered pair $(2,12)$ is a solution of the given system.