Q. 397 - Intermediate Algebra

Question

Determine Whether an Ordered Pair is a Solution of a System of Linear Inequalities
In the following exercises, determine whether each ordered pair is a solution to the system. 

$\left\{\begin{array}{l}4x+y>6\\ 3x-y\le 12\end{array}\right.$

(a) $(2,-1)$

(b) $(3,-2)$

Step-by-Step Solution

Answer

The ordered pair $(2,-1)$ is a solution to the system of inequality $\left\{\begin{array}{l}4x+y>6\\ 3x-y\le 12\end{array}\right.$

The ordered pair $(3,-2)$ is a solution to the system of inequality $\left\{\begin{array}{l}4x+y>6\\ 3x-y\le 12\end{array}\right.$

Part (a) Step 1. Given

The system of inequality $\left\{\begin{array}{l}4x+y>6\\ 3x-y\le 12\end{array}\right.$

To find if the ordered pair $(2,-1)$ is a solution to the system of inequality.

Part (a) Step 2. Substitute the point in the first inequality

Substitute $(2,-1)$ in the inequality,

        $4x+y>6$

$4\left(2\right)+(-1)>6$

           $8-1>6$

                $7>6$ is true.

Part (a) Step 3. Substitute the point in the second inequality

Substitute $(2,-1)$ in the inequality,

         $3x-y\le 12$

$3\left(2\right)-(-1)\le 12$

           $6+1\le 12$

                 $7\le 12$ is true.

The ordered pair $(2,-1)$ made both the inequality true.

So the ordered pair $(2,-1)$ is the solution to the syetm of inequality.

Part (b) Step 1. Given

The system of inequality $\left\{\begin{array}{l}4x+y>6\\ 3x-y\le 12\end{array}\right.$

To find if the ordered pair $(3,-2)$ is the solution to the system of inequality.

Part (b) Step 2. Substitute the point in the first inequality

Substitute $(3,-2)$ in the first inequality,

$4\left(3\right)+(-2)>6$

        $12-2>6$

              $10>6$ is true.

Part (b) Step 3. Substitute the point in the second inequality

Substitute $(3,-2)$ in the inequality,

        $3x-y\le 12$

$3\left(3\right)-(-2)\le 12$

           $9+2\le 12$

              $11\le 12$ is true.

An ordered pair $(3,-2)$ made both the inequality true.

So the ordered pair $(3,-2)$ is a solution to the system of inequality.