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Solution of x-y+z=4 ; x-2 y+2 z=9 and 2 x+y+3 z=1 is

Options

  1. Ax=-4 ; y=-3 ; z=2
  2. Bx=-1 ; y=-3 ; z=2
  3. Cx=2 ; y=4 ; z=6
  4. Dx=3 ; y=6 ; z=9

Correct answer

B. x=-1 ; y=-3 ; z=2

Step-by-step solution

The given system of linear equations is: (1) x - y + z = 4 (2) x - 2y + 2z = 9 (3) 2x + y + 3z = 1 Subtract equation (1) from equation (2): (x - 2y + 2z) - (x - y + z) = 9 - 4 -y + z = 5 --- (4) Multiply equation (1) by 2 and subtract from equation (3): (2x + y + 3z) - 2(x - y + z) = 1 - 2(4) 2x + y + 3z - 2x + 2y - 2z = 1 - 8 3y + z = -7 --- (5) Subtract equation (4) from equation (5): (3y + z) - (-y + z) = -7 - 5 4y = -12 y = -3 Substitute y = -3 into equation (4): -(-3) + z = 5 3 + z = 5 z = 2 Substitute y = -3

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