Based on the information given in the exercise, you can set up the following System of equations:
[tex]\begin{cases}3p-2q=4 \\ 7p-3q=1\end{cases}[/tex]You can use the Substitution method to find the value of the variable "p" and the variable "q":
- Solve for "q" from the first equation:
[tex]\begin{gathered} 3p-2q=4 \\ -2q=4-3p \\ q=\frac{4}{-2}-(\frac{3p}{-2}) \\ \\ q=-2+\frac{3}{2}p \end{gathered}[/tex]- Substitute the new equation into the second equation:
[tex]\begin{gathered} 7p-3q=1 \\ 7p-3(-2+\frac{3}{2}p)=1 \end{gathered}[/tex]- Solve for "p":
[tex]\begin{gathered} 7p+6-\frac{9}{2}p=1 \\ \\ \frac{5}{2}p=1-6 \\ \\ 5p=(2)(-5) \\ \\ p=\frac{-10}{5} \\ \\ p=-2 \end{gathered}[/tex]- Substitute the value of "p" into the equation
[tex]q=-2+\frac{3}{2}p[/tex]And evaluate. Then:
[tex]\begin{gathered} q=-2+\frac{3}{2}(-2) \\ q=-2-3 \\ q=-5 \end{gathered}[/tex]Now knowing the values of "p" and "q", you can substitute them into this expression:
[tex]4p-5q[/tex]And then evaluate. So, you get:
[tex]4(-2)-5(-5)=-8+25=17[/tex]Therefore:
[tex]4p-5q=17[/tex]The answer is: Option D.
