Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution): a-2b=6 3a-6b=0
Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution): a-2b=6 3a-6b=0

Given,

a-2b=6……. (i)

3a-6b=0……. (ii)

For equation (i),

b=(a-6)/2

When a=6, we have b=(6-6)/2=0

When a=2 we have b=(2-6)/2=-2

Thus, we have the following table giving points on the line a-2b=6

a 6 2
b 0 -2

For equation (ii),

We solve for b:

b=a/2

So, when a=0

b=0/2=0

And, when a=2

b=2/2=1

Thus, we have the following table giving points on the line 3a-6b=0.

a 0 2
b 0 1

 

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

From graph, there is no common point between these two lines.

Hence, the given systems of equations are in-consistent.