Find whether the following pair of linear equations is consistent /inconsistent. If consistent, then obtain the solution graphically: $2x + y - 6 = 0,\ 4x -2y-4=0$.

Given: Pair of linear equation: $2x + y - 6 = 0,\ 4x -2y-4=0$.

To do: To find whether the given pair of linear equations is consistent /inconsistent. If consistent, then obtain the solution graphically.

Solution:

$2x+y-6=0$

$4x-2y-4=0$

$2x+y=6\ \ ...( i)$

$4x-2y=4\ \ ...( ii)$

For equation $( i)$,

$2x+y=6$

$\Rightarrow y=6-2x$

x	0	3
y	6	0

Plot point $( 0,\ 6)$ and $( 3,\ 0)$ on a graph and join then to get equation

$3x+y=6$

For equation $( ii)$,

$4x-2y=4$

$\Rightarrow y=\frac{4x-4}{2}$

x	1	0
y	0	-2

Plot point $( 1,\ 0)$ and $( 0,\ -2)$ on a graph and join them to get equation $4x-2y=0$

$x=2,\ y=2$ is the solution of the given pairs of equation. So the solution is consistent.

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Updated on: 10-Oct-2022

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