Chapter 9.2, Problem 30WE

To determine

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

Answer to Problem 30WE

The solution of the given equations by using substitution method is $x=\frac{61}{13}\text{and}y=\frac{302}{13}$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}2x-\frac{y+2}{2}=22\\ 3x+\frac{y+2}{3}=7\end{array}$

The given equation can be written as,

  $\begin{array}{l}2x-\frac{y+2}{2}=22\\ \frac{4x-y+2}{2}=22\\ 4x-y+2=44\\ 4x-y=42\\ y=4x-42\end{array}$

The another given equation is,

  $3x+\frac{y+2}{3}=7$

Substitute $4x-42$ for $y$ .

  $\begin{array}{l}3x+\frac{y+2}{3}=7\\ 3x+\frac{\left(4x-42\right)+2}{3}=7\\ 3x+\frac{4x-40}{3}=7\\ 9x+4x-40=21\\ 13x=21+40\\ x=\frac{61}{13}\end{array}$

The value of $y$ is calculated as,

  $\begin{array}{l}y=4x-42\\ y=4\left(\frac{61}{13}\right)-42\\ y=\frac{244-546}{13}\\ y=\frac{302}{13}\end{array}$

Thus, the solution of the given equations by using substitution method is $x=\frac{61}{13}\text{and}y=\frac{302}{13}$ .