By the graphical method, find whether the following pair of equations are consistent or not. If consistent, solve them.

3x + y + 4 = 0, 6x-2y + 4 = 0


Given pair of equations is

3x + y + 4 = 0 …(i)


and 6x -2y + 4 = 0…(ii)


comparing with ax + by + c = 0


Here, a1 = , b1 = 1, c1 = 4;


And a2 = 6, b2 = - 2, c2 = 4;


a1 /a2 = 1/2


b1 /b2 = -3/6 = -1/2


c1 /c2 = 1


since a1/a2 b1/b2


so system of equations is consistent with a unique solution.


We have,



When x = 0, then y = - 4


When x = - 1, then y = - 1


When x = - 2, then y = 2




0



- 1



- 2



y



- 4



- 1



2



Points



B



C



A



and




When x = 0, then y = 2


When x = - 1,then y = - 1


When x = 1,then y = 5




- 1



0



1



y



- 1



2



5



Points



C



Q



P



Plotting the points B(0, - 4) and A( - 2,2),we get the straight tine AB. Plotting the points Q(0,2) and P(1,5) we get the straight line PQ. The lines AB and PQ intersect at C (-1, -1).



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