Show graphically that each one of the following systems of equations is inconsistent (i.e. has no solution):

$x\ –\ 2y\ =\ 6$
$3x\ –\ 6y\ =\ 0$

Given:

The given system of equations is:

$x\ –\ 2y\ =\ 6$

$3x\ –\ 6y\ =\ 0$

To do:

We have to show that the above system of equations is inconsistent.

Solution:

The given pair of equations are:

$x\ -\ 2y\ -\ 6\ =\ 0$....(i)

$2y=x-6$

$y=\frac{x-6}{2}$

$3x\ -\ 6y\ =\ 0$....(ii)

$6y=3x$

$y=\frac{3x}{6}=\frac{x}{2}$

To represent the above equations graphically we need at least two solutions for each of the equations.

For equation (i),

If $x=6$ then $y=\frac{6-6}{2}=\frac{0}{5}=0$

If $x=2$ then $y=\frac{2-6}{2}=\frac{-4}{2}=-2$

$x$	$6$	$2$
$y=\frac{x-6}{2}$	$0$	$-2$

For equation (ii),

If $x=0$ then $y=\frac{0}{2}=0$

If $x=2$ then $y=\frac{2}{2}=1$

$x$	$0$	$2$
$y=\frac{x}{2}$	$0$	$1$

The above situation can be plotted graphically as below:

The lines AB and PQ represent the equations $x-2y-6=0$ and $3x-6y=0$.

As we can see, there is no common point between the two lines.

Hence, the given system of equations is inconsistent.

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Updated on: 10-Oct-2022

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Show graphically that each one of the following systems of equations is inconsistent (i.e. has no solution):$x\ –\ 2y\ =\ 6$ $3x\ –\ 6y\ =\ 0$