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AP EAMCET2016MathematicsStraight Lines

The equations x-y+2 z=43 x+y+4 z=6x+y+z=1 have

Options

  1. Aunique solution
  2. Binfinitely many solutions
  3. Cno solution
  4. Dtwo solutions

Correct answer

B. infinitely many solutions

Step-by-step solution

Given equations, x-y+2 z=4 aligned & 3 x+y+4 z=6 & x+y+z=1 aligned aligned & Let = | array ccc 1 & -1 & 2 3 & 1 & 4 1 & 1 & 1 array | & =1(1-4)+1(3-4)+2(3-1) & =-3-1+4=0 & and ₁= | array ccc 4 & -1 & 2 6 & 1 & 4 1 & 1 & 1 array | & =4(1-4)+1(6-4)+2(6-1) & =-12+2+10=0 aligned Now, =0 and ₁=0 These equations have infinitely many solutions.

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