Chapter 9.2, Problem 28WE

To determine

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

Answer to Problem 28WE

The solution of the given equations by using substitution method is $d=3\text{and}e=-1$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}\frac{3d+e}{4}=\frac{d+1}{2}\\ \frac{d-e}{4}=1\end{array}$

The given equation can be written as,

  $\begin{array}{l}\frac{3d+e}{4}=\frac{d+1}{2}\\ 6d+2e=4d+4\\ 6d-4d=4-2e\\ d=\frac{4-2e}{2}\\ d=2-e\end{array}$

The another given equation is,

  $\frac{d-e}{4}=1$

Substitute $2-e$ for $d$ .

  $\begin{array}{l}\frac{d-e}{4}=1\\ \frac{\left(2-e\right)-e}{4}=1\\ 2-2e=4\\ e=-1\end{array}$

The value of $d$ is calculated as,

  $\begin{array}{c}d=2-e\\ =2-\left(-1\right)\\ =3\end{array}$

Thus, the solution of the given equations by using substitution method is $d=3\text{and}e=-1$ .