Question

Find the value of athat makes the ordered pair a solution of the equation.

$4x-7y=19;\left(-4,a\right)$

Short answer

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

Step-by-step solution

Step 1. Given Information.

An equation: $4x-7y=19$ and the point: $(-4,a)$

Step 2. Calculation.

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

$\begin{array}{c}4x-7y=19(\text{Givenequation)}\\ 4(-4)-7a=19\left(\text{Substituting}x=-4\text{and}y=a\right)\\ -16-7a=19\\ -16+16-7a=19+16\left(\text{Adding16onbothsides}\right)\\ -7a=35\\ \frac{-7a}{-7}=\frac{35}{-7}\left(\text{Dividingbothsidesby}-7\right)\\ a=-5\end{array}$

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

Step 3. Conclusion.

The value of a would be $-5$.