Chapter 2, Problem 5AR

To determine

To solve the given system of equations by substitution method.

Answer to Problem 5AR

  $x=28,y=4$

Explanation of Solution

Given:

  $\begin{array}{l}4x-5y=92\\ x=7y\end{array}$

Calculation:

  $\begin{array}{l}4x-5y=92\to \left(1\right)\\ x=7y\to \left(2\right)\end{array}$

Now put $x=7y$ inequation (1), we get

  $\begin{array}{l}4\left(7y\right)-5y=92\\ \Rightarrow 28y-5y=92\\ \Rightarrow 23y=92\\ \Rightarrow y=4\end{array}$

Now put $y=4$ in equation (2), we get

  $\begin{array}{l}x=7\left(4\right)\\ \Rightarrow x=28\end{array}$

Therefore the solution is,

  $x=28,y=4$