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

Question

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

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$$a+8b+7c=0$$      $$9a+2b+3c=0$$,   $$a+b+c=07b+6c=0$$,     $$7a+c=0b=$$−$$6c7$$,        $$a=$$−$$c7(a$$,b,$$c)lies$$ on the plane $$x+2y+z=6$$⇒$$a+2b+c=6$$⇒−$$c7$$−$$12c7+c=6$$⇒$$c=$$−$$7$$,     $$b=6$$,    $$a=1$$∴ $$2a+b+c=$$  $$2+6$$−$$7=1$$

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

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

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