Question

13. If ab-b+1=0, bc-C+1 =0,
then abc+ac-a=?
(a)3
(c)8
(d)-5
(b)-2

Answer 1

Answer:

Problem 1 Two of the following systems of equations have solution (1;3). Find them out by checking.

a) \displaystyle \begin{array}{|l} x + y = 5 \\ 2x - y = 7; \end{array}

x+y=5

2x−y=7;

Answer 2

SOLUTION

TO CHOOSE THE CORRECT OPTION

If ab - b + 1 = 0, bc- c + 1 = 0, then abc + ac - a =

(a) 3

(b) -2

(c) 8

(d) -5

EVALUATION

Here it is given that

ab - b + 1 = 0 - - - - - - - (1)

bc - c + 1 = 0 - - - - - - - (2)

From Equation (1) we get

$\sf{b - ab = 1}$

$\sf{ \implies \: b(1 - a) = 1}$

$\displaystyle \: \sf{ \implies \: b = \frac{1}{1 - a} }$

Putting the value of b in Equation (2) we get

$\displaystyle \: \sf{ \frac{c}{1 - a} - c + 1 = 0 }$

$\displaystyle \: \sf{ \implies \: \frac{c - c + ac + 1 - a}{1 - a}= 0 }$

$\displaystyle \: \sf{ \implies \: ac + 1 - a= 0 }$

Now

$\displaystyle \sf{abc + ac - a }$

$\displaystyle \sf{ = c(b - 1) + ac - a } \: \: (from \: 1)$

$\displaystyle \sf{ = bc -c + ac - a } \: \:$

$\sf{ = - 1 - 1 \: \: \: ( \: from \: 2 \: and \: 3 \: )}$

$= - 2$

FINAL ANSWER

Hence the correct option is (b) - 2

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