Chapter 9.1, Problem 10WE

To determine

To find: The solution of the given two linear equations by the graphing method.

Answer to Problem 10WE

The given system has no solution.

Explanation of Solution

Given:

The given equations are:

  $\begin{array}{c}2y-x=2\dots \left(1\right)\\ x-2y=8\dots \left(2\right)\end{array}$

To solve the given equations by graphing method, first, make the tables of the corresponding values of $y$ after substituting the randomly selected values of $x$ in the given equations.

The table for the equation $2y-x=2$ is given as:

Table1

$x$	$0$	$-2$
$y$	$1$	$0$

The table for the equation $x-2y=8$ is given as:

Table2

$x$	$0$	$8$
$y$	$-4$	$0$

Plot all the ordered pairs that shows in the table1 and table2 and hence join them to make the lines in the coordinate plane.

So the graph is given as:

  

As the above graph shows that the graphs of the given two equations are parallel.

Therefore, the given system has no solution.