Chapter 6.2, Problem 20PPS

To determine

To find: Values of x and y.

Answer to Problem 20PPS

  $\begin{array}{l}x=2\\ y=5\end{array}$

Explanation of Solution

Given information:

  $\begin{array}{l}5x-y=5\\ -x+3y=13\end{array}$

  $5x-y=5$ ----(1)

  $-x+3y=13$

$\Rightarrow x=3y-13$ ------(2)

Substitute the value of $x$ from equation-(2) in equation-(1)

We get

  $\begin{array}{l}5x-y=5\\ \Rightarrow 5\left(3y-13\right)-y=5\\ \Rightarrow 5\left(3y\right)-5\left(13\right)-y=5\\ \Rightarrow 15y-65-y=5\\ \Rightarrow 15y-y=65+5\\ \Rightarrow 14y=70\\ \Rightarrow y=\frac{70}{14}\\ \Rightarrow y=5\end{array}$

Substitute value of $y$ in equation-(2)

We get

  $\begin{array}{l}x=3y-13\\ \Rightarrow x=3\left(5\right)-13\\ \Rightarrow x=15-13\\ \Rightarrow x=2\end{array}$

Therefore, values of x and y are

  $\begin{array}{l}x=2\\ y=5\end{array}$