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

Question

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 (A) (- 7, - 4) (B) (- 4, 0) (C) (0, 3) (D) (3, 6)

Tardigrade Admin · Accepted Answer

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) ⇒ b=-5 .

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

(- 7, - 4)

(- 4, 0)

(0, 3)

(3, 6)

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

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