Chapter 6.4, Problem 16PPE

To determine

To solve: The system of linear equations using any of the method and explain the choice.

Answer to Problem 16PPE

x = $\frac{25}{6}$ and y = $-\frac{23}{12}$

Explanation of Solution

Given information:

The equations $5x+2y=17$ and $x-2y=8$

Calculation:

Since, in the given system of linear equations value second term i.e. 2y and −2y can be cancelled out easily. Therefore it is best to use the elimination method to solve these set of equations.

Now add equation $5x+2y=17$ and $x-2y=8$ to obtain

  $\begin{array}{l}5x+2y=17\\ \underset{\_}{x-2y=8}\\ 6x+0=25\end{array}$

Now simplify above equation.

  $\begin{array}{l}6x+0=25\\ \Rightarrow x=\frac{25}{6}\end{array}$

Use above value ofx in equation $x-2y=8$

  $\begin{array}{c}\frac{25}{6}-2y=8\\ -2y=8-\frac{25}{6}\\ -2y=\frac{48-25}{6}\\ -2y=\frac{23}{6}\\ y=-\frac{23}{12}\end{array}$

Therefore the solution is x = $\frac{25}{6}$ and y = $-\frac{23}{12}$ .