Check whether the following equations are consistent or inconsistent , solve them graphically 2x - 3y = 8

Solution

The given equations are 2x - 3y = 8 and 4x - 6y = 9
They can be written as 2x - 3y -8 = 0 and 4x - 6y - 9 = 0

Comparing these equations with a1x+b1y+c1=0 and a2x+b2y+c2=0, we get:

a1=2,b1=−3,and c1=−8
a2=4,b2=−6and c2=−9

a1a2=24=12

b1b2=−3−6=12 and

c1c2=−8−9=89

Hence, a1a2=b1b2≠c1c2

Therefore, these linear equations represent parallel lines and thus have no possible solution.
Hence, the pair of linear equations is inconsistent.