If the system of linear equations x - 4 y + 7 z = g ; 3 y - 5 z = h ; - 2 x + 5 y - 9 z = k is consistent,…

If the system of linear equations x-4y+7z=g; 3y-5z=h; -2x+5y-9z=k is consistent, then:
  1. g+h+2k=0
  2. g+2h+k=0
  3. 2g+h+k=0
  4. g+h+k=0

Solution

x-4y+7z=g ...(i)

3y-5z=h ...(ii)

-2x+5y-9z=k ...(iii)

(i) + (ii), we get

x-y+2z=g+h ...(iv)

(ii) - (iii), we get

2x-2y+4z=h-k

⇒   x-y+2z=h-k2 ...(v)

Since, coefficient of x,y,z in (iv) and (v) are same. Hence, for system to be consistent

g+h=h-k2

⇒   2g+2h=h-k

⇒   2g+h+k=0

Asked in: JEE Main 2019 (09 Jan Shift 2)

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