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JEE Main20262 April 2026Evening ShiftMathematicsDeterminantsActual

If the system of equations x + 5y + 6z = 4 , 2x + 3y + 4z = 7 , x + 6y + az = b has infinitely many solutions, then the point (a, b) lies on the line

Options

  1. Ay - x = 3
  2. Bx - y = 3
  3. Cx + y = 11
  4. Dx + y = 12

Correct answer

B. x - y = 3

Step-by-step solution

For the given system of equations to have infinitely many solutions, the determinant of the coefficient matrix must be zero, = 0 . = vmatrix 1 & 5 & 6 2 & 3 & 4 1 & 6 & a vmatrix = 0 Expanding along the first row: 1(3a - 24) - 5(2a - 4) + 6(12 - 3) = 0 3a - 24 - 10a + 20 + 54 = 0 -7a + 50 = 0 a = 50 7 For infinitely many solutions, we must also have _z = 0 . _z = vmatrix 1 & 5 & 4 2 & 3 & 7 1 & 6 & b vmatrix = 0 Expanding along the first row: 1(3b - 42) - 5(2b - 7) + 4(12 - 3) = 0 3b - 42 - 10b + 35 + 36 = 0 -7b +

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