Question 65654
1. 2x – y = 4	

   2x –y = 6


ANSWER:

FIRST OF ALL REWRITE THESE EQUATIONS IN TERMS OF X,


==> 2x – 4 = y	

     2x –6 =  y


Now give arbitrary values for x and find corresponding values of y.


Using these values plot the graph for these two equations.


Then the graph comes like this.



 

{{{ graph( 500, 500, -10, 10, -10, 10, 2x-4, 2x-6) }}}






 Since two graphs are parellel, these two equations have no solution.




2.  X –2y = 8


   3x –2y = 12


Follow the same procedure as above,


we have equations,



y = x/2 -4  and


y = (3/2)x - 6



Now find out values of y corresponding the values of x.


Using these values plot the graph...



Then the graph comes like this,



 {{{ graph( 500, 500, -10, 10, -10, 10, x/2 -4, (3/2)x-6) }}}






Here two lines intersect at a point.  Draw lines perpendicular to x axis and y axis.

At X axis we have the point 2 and on the Y axis we have -3

So solution for these equations is ( 2, -3)




3. 3x –6y = 9


   X –2y = 3



Here equations become,


y = (1/2)x - 3/2 and


y =(x/2) - (3/2)


Find out values of x and y and plot the graph.


Then the graph cpmes like this,



{{{ graph( 500, 500, -10, 10, -10, 10, (1/2)x-3/2, (x/2)-(3/2)) }}} 




Here we can see that both the lines overlap each other, 
that means two equations represent the same line.




Hope you Understood.



Regards.


praseenakos@yahoo.co.in