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JEE Main 20199 JanuaryEvening Shift
Exam
JEE Main
Year
2019
Date
9 January
Shift
Evening Shift
Subject
Mathematics
Chapter
Determinants

JEE Main 2019 · 9 January · Evening Shift · Mathematics · Determinants

If the system of linear equations x - 4y + 7z = g ; 3y - 5z = h ; -...

If the system of linear equations x−4y+7z=gx - 4y + 7z = g; 3y−5z=h3y - 5z = h; −2x+5y−9z=k- 2x + 5y - 9z = k is consistent, then:

Options

  1. Ag+h+2k=0g + h + 2k = 0
  2. Bg+2h+k=0g + 2h + k = 0
  3. C2g+h+k=02g + h + k = 0
  4. Dg+h+k=0g + h + k = 0

Correct answer

C. 2g+h+k=02g + h + k = 0

Step-by-step solution

x−4y+7z=gx - 4y + 7z = g ...(i)

3y−5z=h3y - 5z = h ...(ii)

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

(i) + (ii), we get

x−y+2z=g+hx - y + 2z = g + h ...(iv)

(ii) - (iii), we get

2x−2y+4z=h−k2x - 2y + 4z = h - k

⇒x−y+2z=h−k2⇒ x - y + 2z = \dfrac{h - k}{2} ...(v)

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

g+h=h−k2g + h = \dfrac{h - k}{2}

⇒2g+2h=h−k⇒ 2g + 2h = h - k

⇒2g+h+k=0⇒ 2g + h + k = 0
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