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If the straight lines x+y-2-0,2x-y+1=0 a...

If the straight lines `x+y-2-0,2x-y+1=0` and `a x+b y-c=0` are concurrent, then the family of lines `2a x+3b y+c=0(a , b , c` are nonzero) is concurrent at (a) `(2,3)` (b) `(1/2,1/3)` (c) `(-1/6,-5/9)` (d) `(2/3,-7/5)`

Text Solution

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`|{:(1,1,-2),(2,-1,1),(a,b,-c):}| = 0`
or a+5b-3c=0
or `-(a)/(3)-(5)/(3)b+c = 0`
Hence, 2ax+3by+c=0 is concurrent at 2x = -1/3 and 3y=-5/3.
So, x=-1/6, y=-5/9.
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