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Q.

If the ordered tried $(α, β, γ)$ is a solution of the system of linear equations $3 x - 2 y + z + 6 = 0, 2 x + 5 y - 3 z = 2$ , $4 x - 9 y + 5 z + 14 = 0$ then the straight line in the xy-plane which contains the point $(α, β)$ is

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a

$31 x + 15 y = 76$

b

$209 x - 19 y + 304 = 0$

c

$79 x - 53 y + 14 = 0$

d

$11x - 99y + 56 = 0$

answer is B.

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Detailed Solution

detailed_solution_thumbnail

Given system has infinitely many solutions
$α = \frac{k - 26}{19}, β = \frac{11 k + 18}{19}$ and verify

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If the ordered tried (α,β,γ) is a solution of the system of linear equations 3x−2y+z+6=0,2x+5y−3z=2 , 4x−9y+5z+14=0 then the straight line in the xy-plane which contains the point α,β is