Question

5. For what value(s) of p are the equations
px + 8y = 14 and (p+3)x + 12y = 21 not inconsistent?
h
an​

Answer 1

The equations are never inconsistent.

Inconsistent equations are those which never meet in the 2-D plane.

Here we have 2 lines which can depict in the plane.

For 2 equations a1x+b1y + c1=0 and a2x + b2y + c2 = 0.

They are inconsistent when a1/a2 = b1/b2 is not = c1/c2.

However here in this we have that:-

p+3/p = 12/8 = 21/14.

or p+3/p = 3/2 = 3/2.

Hence these lines always intersect at (0,3/2).

=> for any value of p they will always intersect.

Hence these line are consistent and never inconsistent.