Answer :

3x + 2y = 6 …(1)

12x + 8y = 24 …(2)


Let us express the equations (1) and (2) in the form of


ax + by +c = 0 where a and b can’t be 0 at the same time.


[In the first equation, we use a1, b1, c1 and in second equation, we use a2, b2, c2 ]


3x + 2y = 6 12x + 8y = 24


3x + 2y + (-6) = 0 12x + 8y + (-24) = 0


Or 3 × x + 2 × y + (-6) = 0 or, 12 × x + 8 × y + (-24) = 0


Here a1 = 3, b1 = 2, c1 = -6 and a2 = 12, b2 = 8, c2 = -24


Comparing the ratio of , we get


, and


Here . Therefore, it is solvable and has infinite common solutions. Lines will overlap.


Now, plot the lines on graph,


3x + 2y = 6 y = ... equation (i)



Equation (i) will be plotted as line AB.


12x + 8y = 24 y = ... equation (ii)



Equation (ii) will be plotted as line CD.



Here in the graph also, we can see that both lines are overlapping on each other. Therefore it has infinite common solutions.


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