Question

0. If ambilthen the system of equations ax + by = cx + y = 1
has no solution
B) has a nie solution
Clhas infinitely many solutions
be eclected​

Answer 1

Step-by-step explanation:

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Answer 2

ANSWER

Given system of eqautions has non-trivial solution.

⇒

∣

∣

∣

∣

∣

∣

∣

∣

a

b

−1

a

−1

c

−1

b

c

∣

∣

∣

∣

∣

∣

∣

∣

=0

⇒a(−c−bc)−a(bc+b)−(bc−1)=0

⇒ab+bc+ca+2abc=1 -----(1)

Now,

1+a

1

+

1+b

1

+

1+c

1

=

(1+a)(1+b)(1+c)

(1+b)(1+c)+(1+a)(1+c)+(1+a)(1+b)

=

1+a+b+c+ab+bc+ca+abc

3+2a+2b+2c+ab+bc+ca

rewriting numerator using (1) gives

=

1+a+b+c+ab+bc+ca+abc

2(1+a+b+c+ab+bc+ca+abc)

=2

Hence, option A.