Show graphically that each of the following given systems of equations has infinitely many solutions:

x - 2y = 5, 3x - 6y = 15.

For equation, x – 2y = 5


First, take x = 0 and find the value of y.


Then, take y = 0 and find the value of x.


x



0



5



y



- 5/2



0



Now similarly solve for equation, 3x – 6y = 15


x



0



5



y



- 5/2



0



Plot the values in a graph and find the intersecting point for the solution.



The lines coincide on each other, this indicates that there are number of intersection points on the line since a line consists of infinite points.


Hence, the graph shows that the system of equations have infinite number of solutions.


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