Answer:
The solution to the system of equations
Hence, the value of q = -50
Step-by-step explanation:
Given the system of equations
[tex]\begin{bmatrix}-16p-2q=100\\ p-4q=200\end{bmatrix}[/tex]
solving to determine the value of q
Multiply p − 4q = 200 by 16: [tex]16p-64q=3200[/tex]
[tex]\begin{bmatrix}-16p-2q=100\\ 16p-64q=3200\end{bmatrix}[/tex]
so adding the equations
[tex]16p-64q=3200[/tex]
[tex]+[/tex]
[tex]\underline{-16p-2q=100}[/tex]
[tex]-66q=3300[/tex]
so
[tex]\begin{bmatrix}-16p-2q=100\\ -66q=3300\end{bmatrix}[/tex]
solve -66q = 3300
[tex]-66q=3300[/tex]
Divide both sides by -66
[tex]\frac{-66q}{-66}=\frac{3300}{-66}[/tex]
[tex]q=-50[/tex]
substituting q = -50 in −16p − 2q = 100
[tex]-16p-2\left(-50\right)=100[/tex]
[tex]-16p+100=100[/tex]
Subtract 100 from both sides
[tex]-16p+100-100=100-100[/tex]
Simplify
[tex]-16p=0[/tex]
Divide both sides by -16
[tex]\frac{-16p}{-16}=\frac{0}{-16}[/tex]
[tex]p=0[/tex]
Thus, the solution to the system of equations
Hence, the value of q = -50
