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

2x + 3y = 6, 4x + 6y = 12.

For equation, 2x + 3y = 6


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


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


x



0



3



y



2



0



Now similarly solve for equation, 4x + 6y = 12


x



0



3



y



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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