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

x + y = 3, 3x + 3y = 9


Given pair of equations is

x + y = 3 …(i)


and 3x + 3y = 9 …(ii)


On comparing with ax + by + c = 0


Here, a1 = 1, b1 = 1, c1 = - 3;


And a2 = 3, b2 = 3, c2 = - 9;


a1 /a2 = 1/3


b1 /b2 = 1/3


c1 /c2 = 1/3


Here, a1/a2 = b1/b2 = c1/c2, i.e. coincident lines


Hence, the given pair of linear equations is coincident and having infinitely many solutions.


The given pair of linear equations is consistent.


Now,


If x = 0 then y = 3, If x = 3, then y = 0.


x



0



3



y



3



0



Points



A



B



and


If x = 0 then y = 3, if x = 1, then y = 2, and if x = 3, then y = 0.


x



0



1



3



y



3



2



0



Points



C



D



E




Plotting the points A(0, 3) and B(3, 0), we get the line AB. Again, plotting the points C(0, 3) and D(1, 2) and E(3, 0), we get the line CDE.


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