Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution): 3a-4b-1=0 2a-(8/3)b+5=0
Show graphically that each one of the following systems of equations is in-consistent (i.e. has no solution): 3a-4b-1=0 2a-(8/3)b+5=0

Given,

3a-4b-1=0……. (i)

2a-(8/3)b+5=0……. (ii)

From equation (i),

b=(3a-1)/4

When a=-1, we have b=(3(-1)-1)/4=-1

When a=3, we have b=(3(3)-1)/4=2

a -1 3
b -1 2

Thus, we have the following table giving points on the line 3a-4b-1=0

From equation (ii),

Solve for b:

b=(6a+15)/8

So, when a=-2.5

b=(6(-2.5)+15)/8=0

And, when a=1.5

b=(6(1.5)+15)/8=3

Thus we have the following table giving points on the line 2a-(8/3)b+5=0

a -2.5 1.5
b 0 3

 

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

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

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