Chapter 9.2, Problem 22WE

To determine

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

Answer to Problem 22WE

The solution of the given equations by using substitution method is $a=-1\text{and}b=\frac{2}{3}$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}3b-2a=4\\ \frac{b}{2}-\frac{2a}{3}=1\end{array}$

The given equation can be written as,

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

The another given equation is,

  $3b-2a=4$

Substitute $\frac{6+4a}{3}$ for $b$ .

  $\begin{array}{l}3b-2a=4\\ 3\left(\frac{6+4a}{3}\right)-2a=4\\ 6+4a-2a=4\\ 6+2a=4\\ a=-1\end{array}$

The value of $b$ is calculated as,

  $\begin{array}{c}b=\frac{6+4a}{3}\\ =\frac{6+4\left(-1\right)}{3}\\ =\frac{2}{3}\end{array}$

Thus, the solution of the given equations by using substitution method is $a=-1\text{and}b=\frac{2}{3}$ .