Chapter 8.2, Problem 37E

To determine

To find:

The value of a that makes the ordered pair $(-4,a)$ a solution of the given equation.

Answer to Problem 37E

The value $a=-5$ would make the ordered pair $(-4,a)$ a solution of the given equation.

Explanation of Solution

Given:

An equation: $4x-7y=19$

Calculation:

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

  $\begin{array}{l}4x-7y=19(\text{Given equation)}\\ 4(-4)-7a=19\left(\text{Substituting }x=-4\text{ and }y=a\right)\\ -16-7a=19\\ -16+16-7a=19+16\left(\text{Adding 16 on both sides}\right)\\ -7a=35\\ \frac{-7a}{-7}=\frac{35}{-7}\left(\text{Dividing both sides by }-7\right)\\ a=-5\end{array}$ .

Therefore, the value of a would be $-5$ .