Q61 / 125 · BITSAT 2012 · Mathematics

The equations $2 x+3 y+4=0 ; 3 x+4 y+6=0$ and $4 x+5 y+8=0$ are

  • Correct answer
    A
    consistent with unique solution
  • B
    inconsistent
  • C
    consistent with infinitely many solutions
  • D
    None of the above

Solution

Consider first two equations: $2 x+3 y=-4 \quad$ and $\quad 3 x+4 y=-6$ We have $\Delta=\left|\begin{array}{ll}2 & 3 \\ 3 & 4\end{array}\right|=-1 \neq 0$ $$ \Delta_{\mathrm{x}}=\left|\begin{array}{ll} -4 & 3 \\ -6 & 4 \end{array}\right|=2 \quad \text { and } \quad \Delta_{\mathrm{y}}=\left|\begin{array}{cc} 2 & -4 \\ 3 & -6 \end{array}\right|=0 $$ $\therefore x=-2$ and $y=0$ Now this solution satisfies the third, so the equations are consistent with unique solution.

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

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