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BITSAT2012MathematicsDeterminantsActual

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

Options

  1. Aconsistent with unique solution
  2. Binconsistent
  3. Cconsistent with infinitely many solutions
  4. DNone of the above

Correct answer

A. consistent with unique solution

Step-by-step solution

Consider first two equations: 2 x+3 y=-4 and 3 x+4 y=-6 We have = | array ll 2 & 3 3 & 4 array |=-1 0 _ x = | array ll -4 & 3 -6 & 4 array |=2 and _ y = | array cc 2 & -4 3 & -6 array |=0 x=-2 and y=0 Now this solution satisfies the third, so the equations are consistent with unique solution.

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