Question

If (p, q) is the solution to the system of equations, what is the value of q?

Answer 1

Answer:

The solution to the system of equations

• p = 0

• q = -50

Hence, the value of q = -50

Step-by-step explanation:

Given the system of equations

$\begin{bmatrix}-16p-2q=100\\ p-4q=200\end{bmatrix}$

solving to determine the value of q

Multiply p − 4q = 200 by 16:      $16p-64q=3200$

$\begin{bmatrix}-16p-2q=100\\ 16p-64q=3200\end{bmatrix}$

so adding the equations

$16p-64q=3200$

$+$

$\underline{-16p-2q=100}$

$-66q=3300$

so

$\begin{bmatrix}-16p-2q=100\\ -66q=3300\end{bmatrix}$

solve -66q = 3300

$-66q=3300$

Divide both sides by -66

$\frac{-66q}{-66}=\frac{3300}{-66}$

$q=-50$

substituting q = -50 in −16p − 2q = 100

$-16p-2\left(-50\right)=100$

$-16p+100=100$

Subtract 100 from both sides

$-16p+100-100=100-100$

Simplify

$-16p=0$

Divide both sides by -16

$\frac{-16p}{-16}=\frac{0}{-16}$

$p=0$

Thus, the solution to the system of equations

• p = 0

• q = -50

Hence, the value of q = -50