# Show that the linear equation x+y=5,2x+2y=10 is consistent or inconsistent

$x+y=5.....(1)$
$2x+2y=10.....(2 )$
$\Rightarrow x+y=5\: and\: y=5-x$
By hit and trail method,
Putting the value of x as 0 we get the value of y as 5 and $(0,5)$
Again putting the value of x as 3 we get the value of y as 2 $(3,2)$
Now by Graph we get the equation as $x+y=5$
Multiplying the above equation by 2,we get
$2x+2y=10$
$\Rightarrow 2y=(10-2x)$
$\Rightarrow y=\frac{(10-2x)}{2}=5-x........(3)$
Now putting the value of x as 5 we get the value of y as 0 and
Again putting the value of x as 2 we get the value of y as 3.
So, the equation is consistent and has infinitely many solution.

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