JEE Main 2017 · 9 Apr · Shift 1 · Mathematics Q65

← JEE Main 2017 · 9 Apr · Shift 1

MathematicsSingle correct+4 / -1Question 65 of 90

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 :

−1

Answer and worked solution

Official answer: C

Subtracting the third equation from the first, $7y+6z=0$ . Then $x=-y-z$ , and the second equation holds. The solutions are $(a,b,c)=k(1,6,-7)$ . On the plane, $k(1+12-7)=6$ , so $k=1$ and $2a+b+c=2+6-7=1$ .

Topics:Systems of linear equations

← Previous question Next question →

JEE Main 2017 · 9 Apr · Shift 1, Mathematics question 65