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

Question

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

Tardigrade Admin · Accepted Answer

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) ⇒ 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