Chapter 9.2, Problem 29WE

To determine

To find: The solution of the given equations by using substitution method.

Answer to Problem 29WE

The solution of the given equations by using substitution method is $p=2\text{and}q=-6$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}\frac{3p-q}{4}=p+1\\ \frac{5p+q}{2}=p\end{array}$

The given equation can be written as,

  $\begin{array}{l}\frac{3p-q}{4}=p+1\\ 3p-q=4p+4\\ -p-q=4\\ p=-4-q\end{array}$

The another given equation is,

  $\begin{array}{l}\frac{5p+q}{2}=p\\ 5p+q=2p\\ 3p=-q\end{array}$

Substitute $-4-q$ for $p$ .

  $\begin{array}{l}3\left(-4-q\right)=-q\\ -12-3q=-q\\ -2q=12\\ q=-6\end{array}$

The value of $p$ is calculated as,

  $\begin{array}{c}p=-4-q\\ =-4-\left(-6\right)\\ =-4+6\\ =2\end{array}$

Thus, the solution of the given equations by using substitution method is $p=2\text{and}q=-6$ .