Chapter 8.8, Problem 39E

To determine

Which ordered pair is nota solution of the linear system $x-3y=-12\text{ and }-3x+9y=36$ ?

Answer to Problem 39E

The ordered pair $(-3,2)$ is not a solution for the given system and option F is the correct choice.

Explanation of Solution

Given:

Four choices:

  $\text{F}\text{. (}-3,2)\text{ G}\text{. (0,4) H}\text{. (}3,5)\text{ I}\text{. (}6,6)$

Calculation:

First of all, we will divide our 2^nd equation by 3 as shown below:

  $\begin{array}{l}-3x+9y=36\left(\text{Given 2nd equation}\right)\\ \frac{-3x}{-3}+\frac{9y}{-3}=\frac{36}{-3}\left(\text{Dividing both sides by }-3\right)\\ x-3y=-12\end{array}$

We can see that both equations represent same lines.

To check which ordered pair is not a solution for the given system, we will substitute coordinates of each given point in equation $x-3y=-12$ as shown below:

  $\begin{array}{l}x-3y=-12\left(\text{Given equation}\right)\\ -3-3(2)=-12\left(\text{Substituting }x=-3\text{and }y=2\right)\\ -3-6=-12\\ -9\ne -12\end{array}$

Since thepoint $(-3,2)$ doesn’t satisfy our given system, so the ordered pair $(-3,2)$ is not a solution for the given system.

  $\begin{array}{l}x-3y=-12\left(\text{Given equation}\right)\\ 0-3(4)=-12\left(\text{Substituting }x=0\text{and }y=4\right)\\ 0-12=-12\\ -12=-12\end{array}$

Since the point $(0,4)$ satisfies our given system, so the ordered pair $(0,4)$ is a solution for the given system.

  $\begin{array}{l}x-3y=-12\left(\text{Given equation}\right)\\ 3-3(5)=-12\left(\text{Substituting }x=3\text{and }y=5\right)\\ 3-15=-12\\ -12=-12\end{array}$

Since the point $(3,5)$ satisfies our given system, so the ordered pair $(3,5)$ is a solution for the given system.

  $\begin{array}{l}x-3y=-12\left(\text{Given equation}\right)\\ 6-3(6)=-12\left(\text{Substituting }x=6\text{and }y=6\right)\\ 6-18=-12\\ -12=-12\end{array}$

Since the point $(6,6)$ satisfies our given system, so the ordered pair $(6,6)$ is a solution for the given system.