Chapter 9.2, Problem 24WE

To determine

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

Answer to Problem 24WE

The solution of the given equations by using substitution method is $c=-6\text{and}d=5$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}\frac{c}{2}-\frac{d}{5}=-4\\ \frac{2c}{3}-\frac{3d}{5}=-7\end{array}$

The given equation can be written as,

  $\begin{array}{l}\frac{c}{2}-\frac{d}{5}=-4\\ 5c-2d=-40\\ c=\frac{-40+2d}{5}\end{array}$

The another given equation is,

  $\begin{array}{l}\frac{2c}{3}-\frac{3d}{5}=-7\\ 10c-9d=-105\end{array}$

Substitute $\frac{-40+2d}{5}$ for $c$ .

  $\begin{array}{c}10c-9d=-105\\ 10\left(\frac{-40+2d}{5}\right)-9d=-105\\ 2\left(-40+2d\right)-9d=-105\\ -80+4d-9d=-105\end{array}$

  $\begin{array}{c}-80+4d-9d=-105\\ -5d=-105+80\\ d=\frac{-25}{-5}\\ d=5\end{array}$

The value of $c$ is calculated as,

  $\begin{array}{c}c=\frac{-40+2d}{5}\\ =\frac{-40+2\left(5\right)}{5}\\ =\frac{-30}{5}\\ =-6\end{array}$

Thus, the solution of the given equations by using substitution method is $c=-6\text{and}d=5$ .