Question

If $\vec{a}$ and $\vec{b}$ are non zero, non collinear vectors, and the linear combination $(2 x-y) \vec{a}+4 \vec{b}=5 \vec{a}+(x-2 y) \vec{b}$ holds for real $x$ and $y$ then $x+y$ has the value equal to

Answer 1

$(2 x-y-5) \vec{a}$
$=(x-2 y-4) \vec{b}$
$\therefore 2 x-y=5$ ...(1)
$x-2 y=4$ ...(2)
from (1) and (2)
$2(2 y+4)-y=5$
$\Rightarrow 3 y=-3$
$\Rightarrow y=-1$
and $x=2 ;$
hence $x+y=1 $
$\Rightarrow y=-1$