Determine the equations , is consistent or in-consistent using graphical method

Given,

……. (i)

……. (ii)

For equation (i),

⇒

When , we have

When , we have

Thus, we have the following table giving points on the line

a
b

From equation (ii),

We solve for a:

⇒

So, when

And, when

⇒

Thus, we have the following table giving points on the line

a
b

Graph of the equations (i) and (ii) is as below:

From graph, it can be seen that the two lines intersect at .

Hence, the system of equations is consistent.