Q75 / 150 · MHT CET 2007 · Mathematics

For the equations $$ x+2 y+3 z=1,2 x+y+3 z=2 $$ and $5 x+5 y+9 z=4$

  • Correct answer
    A
    there is only one solution
  • B
    there exists infinitely many solution
  • C
    there is no solution
  • D
    None of the above

Solution

\Delta &=\left|\begin{array}{lll} 1 & 2 & 3 \\ 2 & 1 & 3 \\ 5 & 5 & 9 \end{array}\right| \\ &=1(9-15)-2(18-15)+3(10-5) \\ &=-6-6+15=3 \neq 0 \end{aligned} $$ Hence, the system of equations has a unique solution.

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

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