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Question

If 2x − 3y = 7 and (a + b)x − (a + b − 3)y = 4a + b represent coincident lines, then a and b satisfy the equation

(a) a + 5b = 0
(b) 5a + b = 0
(c) a − 5b = 0
(d) 5a − b = 0

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Solution

The given system of equations are

For coincident lines , infinite number of solution

a1a2=b1b2=c1c2 2a+b=-3-a+b-3=74a+b 2a+b=3a+b-3=74a+b 2a+b-3=3a+b 2a+2b-6=3a+3b 2a+2b-3a-3b=6 -a-b=6 a+b=-6 ---(i)34a+b=7a+b-312a+3b=7a+7b-215a-4b=-21 ---(ii)multiply equation (i) by 5, we get 5a+5b=-30 ---(iii)subtract (ii) from (iii),5a+5b-5a-4b=-30+215a+5b-5a+4b=-99b=-9b=-1substitute b=-1 in equation (1)a+-1=-6a=-6+1 = -5


Option A.:

a+5b=0-5+5-1 = -5-5 = -10 0

Option B:

5a+b=05-5+-1 = -25-1 = -260

Option.C:

a - b = 0

-5 - (-1) = -4 0


None of the option satisfies the values.


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