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

3x - y = 5, 6x - 2y = 10.

For equation, 3x – y = 5


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


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


x



0



5/3



y



- 5



0



Now similarly solve for equation, 6x - 2y = 10


x



0



5/3



y



- 5



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.


23