Show graphically that each of the following given systems of equations is inconsistent, i.e., has no solution:

Question

Show graphically that each of the following given systems of equations is inconsistent, i.e., has no solution: 2x + y = 6, 6x + 3y = 20.

Philoid · Accepted Answer

For equation, 2x + y = 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	6	0

Now similarly solve for equation, 6x + 3y = 20

x	0	10/3
y	20/3	0

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

The set of equations are parallel to each other in the graph.

Parallel lines never meet each other even if they are extended.

Hence, the graph shows that the system of equations have no solutions.