Q55 / 100 · BITSAT 2024 (Memory Based Paper 2) · Mathematics

The equations $x-y+2 z=4$ $3 x+y+4 z=6$ $x+y+z=1$ have

  • A
    unique solution
  • Correct answer
    B
    infinitely many solutions
  • C
    no solution
  • D
    two solutions

Solution

Given equations, $x-y+2 z=4$ $3 x+y+4 z=6$ $x+y+z=1$ Let $\Delta=\left|\begin{array}{ccc}1 & -1 & 2 \\ 3 & 1 & 4 \\ 1 & 1 & 1\end{array}\right|$ $=1(1-4)+1(3-4)+2(3-1)$ $=-3-1+4=0$ and $\Delta_1=\left|\begin{array}{ccc}4 & -1 & 2 \\ 6 & 1 & 4 \\ 1 & 1 & 1\end{array}\right|$ $=4(1-4)+1(6-4)+2(6-1)$ $=-12+2+10=0$ Now, $\Delta=0$ and $\Delta_1=0$ $\therefore$ These equations have infinitely many solutions.

Hence, the correct answer is option: 'B'.

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