Chapter 8.2, Problem 38E

To determine

To find:

The value of a that makes the ordered pair $(a+2,-3)$ a solution of the given equation.

Answer to Problem 38E

The value $a=4$ would make the ordered pair $(a+2,-3)$ a solution of the given equation.

Explanation of Solution

Given:

An equation: $6x+5y=21$

Calculation:

To find the value of a , we will substitute coordinates of given pointin our given equation and solve for a as:

  $\begin{array}{l}6x+5y=21(\text{Given equation)}\\ 6(a+2)+5(-3)=21\left(\text{Substituting }x=a+2\text{ and }y=-3\right)\\ 6a+12-15=21\left(\text{Using distributive property}\right)\\ 6a-3=21\\ 6a-3+3=21+3\left(\text{Adding 3 on both sides}\right)\\ 6a=24\\ \frac{6a}{6}=\frac{24}{6}\left(\text{Dividing both sides by }6\right)\\ a=4\end{array}$

Therefore, the value of a would be $4$ .