Question

1. Is the following pair of linear equations consistent? Justify your answer.

Answer 1

Answer:

Given equation:– 2ax + by = a, 4ax + 2by - 2a = 0

a1 = 2a; b1 = b; c1 = - a & a2 = 4a; b2 = 2b; c2 = - 2a.

For consistence, a1/a2 = b1/b2 = c1/c2 must be equal

• 2a/4a = b/2b = -a/-2a
• 1/2 = 1/2 = 1/2

So, The given equation is consistence.

Answer 2

Yes.

Justification:

Here,

• a1/a2 = 2a/4a = 1/2,
• b1/b2 = b/2b = 1/2,
• c1/c2 = - a/- 2a = 1/2.

∵ a1/a2 = b1/b2 = c1/c2

∴ The given system of equations is consistent.