Chapter 8.2, Problem 55E

To determine

Which ordered pair is not a solution of the equation $5x-4y=7$ .

Answer to Problem 55E

The ordered pair $(-5,-9)$ is not a solution of the equation $5x-4y=7$ .

Explanation of Solution

Given:

Four ordered pairs: $\text{A}\text{. }(-9,-13)\text{ B}\text{. }(-5,-9)\text{ C}\text{. }(7,7)\text{ D}\text{. }(11,12)$

Calculation:

We need to check each ordered pair one by one as shown below:

  $\begin{array}{l}5x-4y=7\left(\text{Given equation}\right)\\ 5(-9)-4(-13)=7\left(\text{Substituting }x=-9\text{ and }y=-13\right)\\ -45+52=7\\ 7=7\end{array}$

Since both sides of equation are equal, therefore, the ordered pair $(-9,-13)$ is a solution for the given equation.

  $\begin{array}{l}5x-4y=7\left(\text{Given equation}\right)\\ 5(-5)-4(-9)=7\left(\text{Substituting }x=-5\text{ and }y=-9\right)\\ -25+36=7\\ 11\ne 7\end{array}$

Since both sides of equation are not equal, therefore, the ordered pair $(-5,-9)$ is not a solution for the given equation and option B is the correct choice.