Question

For what values of a and b does the pair of equations 2x+3y=7
(a-b)x+(a+b)y=3a+b-2

Answer 1

Answer:

So Since no solution exists if :

(a-b)/2 = (a+b)/3

So 3a - 3b = 2a + 2b

So a = 5b

So eqn 2 becomes :

(5b-b)x + (5b+b)y = 3(5a) + b - 2

So 4bx + 6by = 16b-2

Also (a-b)/2 is not equal to (16b-2)/7 [!= means 'not equal to']

on solving : 7a-7b != 32b-4

So 35b- 7b != 32b-4

so b is not equal to 1.

and a is not equal to 5. (5b)

Hence lines coincide if :

a=5

b=1

And no solution exists if :

a=5b

where a is not equal to 5.

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