Chapter 9.2, Problem 27WE

To determine

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

Answer to Problem 27WE

The solution of the given equations by using substitution method is $x=12\text{and}y=8$ .

Explanation of Solution

Given information:

The given equations are,

  $\begin{array}{l}\frac{x+y}{2}=10\\ 2x=3y\end{array}$

The given equation can be written as,

  $\begin{array}{l}\frac{x+y}{2}=10\\ x+y=20\\ x=20-y\end{array}$

The another given equation is,

  $2x=3y$

Substitute $20-y$ for $x$ .

  $\begin{array}{l}2x=3y\\ 2\left(20-y\right)=3y\\ 40-2y=3y\\ -2y-3y=-40\\ y=8\end{array}$

The value of $x$ is calculated as,

  $\begin{array}{c}x=20-y\\ =20-8\\ =12\end{array}$

Thus, the solution of the given equations by using substitution method is $x=12\text{and}y=8$ .