1. Tardigrade
  2. Question
  3. Mathematics
  4. If the system of equations x + 2y + 2z = 1 x - y + 3z = 3 x + 11y - z = b has solutions, then the value of b lies in the interval

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Q. If the system of equations
$x + 2y + 2z = 1$
$x - y + 3z = 3$
$x + 11y - z = b$
has solutions, then the value of b lies in the interval

Determinants

Solution:

$x + 2y + 2z = 1$ ....(1)
$x - y + 3z = 3$ ....(2)
$x + 11y - z = b$ ....(3)
From (1) and (2)
$z = 2 + 3y$ and $x = - 8y - 3$
Put in equation (3)
$\Rightarrow b=-5 . $