Q 284. - Intermediate Algebra

Question

In the following exercise, determine whether each ordered pair is a solution to the system.  

$\left\{\begin{array}{l}7x+2y>14\\ 5x-y\le 8\end{array}\right.$

$$\begin{gathered} ⓐ (2, 3) \\ ⓑ (7, -1) \end{gathered}$$

Step-by-Step Solution

Answer

Part (a).  The ordered pair $\left(2,3\right)$ is the solution of the given system of inequalities .

Part (b)  The ordered pair $\left(7,-1\right)$ is not the solution of the given system of inequalities 

Part (a) Step 1 . Substitute ( 2 , 3 ) in the given system of inequalities.

Substituting $\left(2,3\right)$ in the inequality $7x+2y>14$:

This is true.

Again substituting $\left(2,3\right)$ in the inequality $5x-y\le 8$:

$$\begin{gathered} 5x-y\le 8 \\ 5\times 2-3\le 8 \\ 7\le 8 \end{gathered}$$

This is also true.

Thus, the ordered pair $\left(2,3\right)$ is a solution.

Part (b). Step 1. Substitute 7 , - 1 in the given system of inequalities.

Substituing $\left(7,-1\right)$ in the inequality

$7x + 2y > 14$ :

$$\begin{gathered} 7x + 2y > 14 \\ 7\times 7+2\times -1>14 \\ 49-2>14 \\ 47>14 \end{gathered}$$

This is true.

Also, substituting $\left(7,-1\right)$ inequality
$5x - y \le 8$:

$$\begin{gathered} 5x - y \le 8 \\ 5\times 7-(-1)\le 8 \\ 35+1\le 8 \\ 36\le 8 \end{gathered}$$

This is not true.

Thus the ordered pair $(7,-1)$ is not a solution.