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

Answers (1)

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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