Linear Equations

Which one of the following conditions must p, q and r satisfy so that the following system of linear simultaneous equations has at least one solution, such that p + q + r ≠ 0?

  • x + 2y - 3z = p
  • 2x + 6y - 11z = q
  • x - 2y + 7z = r
  1. 5p - 2q - r = 0
  2. 5p + 2q + r = 0
  3. 5p + 2q - r = 0
  4. 5p - 2q + r = 0

Answer

It is given that p + q + r ≠ 0

Multiply the first equation by 5, second by -2 and third by -1, the coefficients of x, y and z all add up to zero.

5x + 10y - 15z = 5p

-4x - 12y + 22z = -2q

-x + 2y - 7z = -r

Adding all three equations:

5p - 2q - r = 0

The correct option is A.