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Question

If x=a,y=b,z=c is a solution of the system of linear equations x+8y+7z=0,9x+2y+3z=0,x+y+z=0 such that the point(a,b,c) lies on the plane x+2y+z=6, then 2a+b+c equals.

A
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C
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Solution

The correct option is C 1
x+8y+7z=0 ........(1)
9x+2y+3z=0 .........(2)
x+y+z=0 ........(3)
Multiply eqn. (3) by 3 & subtract from eqn. (2)
9x+2y+3z=0
3x±3y±3z=0
_____________________
6xy=0
_____________________
y=6x .........(4)
Substitute in Eqn (1). we get
x+8(6x)+7z=0
49x+7z=0
7x+z=0
z=7x .........(5)
x=a, y=b.z=c
is the solutions of the system of linear equation
b=6a and c=7a .......(6)
Also, (a, b, c) lies on the plane x+2y+z=6
a+2b+c=6 ........(7)
Substitute eq. (6) in eq(7)
a+2(6a)7a=6
a+12a7a=6
6a=6
a=1
So, b=6 and c=7
2a+b+c=2(1)+67=1.

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