Chapter 9.2, Problem 25WE

To determine

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

Answer to Problem 25WE

The solution of the given equations by using substitution method is $x=94.55\text{and}y=945.45$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}x+y=1000\\ 0.005x+0.06y=57\end{array}$

The given equation can be written as,

  $\begin{array}{l}x+y=1000\\ x=1000-y\end{array}$

The another given equation is,

  $0.005x+0.06y=57$

Substitute $1000-y$ for $x$ .

  $\begin{array}{l}0.005\left(1000-y\right)+0.06y=57\\ 5-0.005y+0.06y=57\\ 0.055y=57-5\\ y=945.45\end{array}$

The value of $x$ is calculated as,

  $\begin{array}{c}x=1000-y\\ =1000-945.45\\ =94.55\end{array}$

Thus, the solution of the given equations by using substitution method is $x=94.55\text{and}y=945.45$ .