Question

If 3p - 2q = 4 and 7p - 39 = 1.then what is 4p - 59 equal to?

Answer 1

Based on the information given in the exercise, you can set up the following System of equations:

`\begin{cases}3p-2q=4 \\ 7p-3q=1\end{cases}`

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:

`\begin{gathered} 3p-2q=4 \\ -2q=4-3p \\ q=(4)/(-2)-((3p)/(-2)) \\ \\ q=-2+(3)/(2)p \end{gathered}`

- Substitute the new equation into the second equation:

`\begin{gathered} 7p-3q=1 \\ 7p-3(-2+(3)/(2)p)=1 \end{gathered}`

- Solve for "p":

`\begin{gathered} 7p+6-(9)/(2)p=1 \\ \\ (5)/(2)p=1-6 \\ \\ 5p=(2)(-5) \\ \\ p=(-10)/(5) \\ \\ p=-2 \end{gathered}`

- Substitute the value of "p" into the equation

`q=-2+(3)/(2)p`

And evaluate. Then:

`\begin{gathered} q=-2+(3)/(2)(-2) \\ q=-2-3 \\ q=-5 \end{gathered}`

Now knowing the values of "p" and "q", you can substitute them into this expression:

`4p-5q`

And then evaluate. So, you get:

`4(-2)-5(-5)=-8+25=17`

Therefore:

`4p-5q=17`

The answer is: Option D.