Given that the vectors a and b are non-collinear, the values of x and y for which the vector equality $2\vec u - \vec v =\vec w$ holds true if $\vec u=x\vec a+2y\vec b,\vec v=-2y\vec a+3x\vec b,\vec w=4\vec a-2\vec b$ are

$x=\frac{10}{7},y=\frac{4}{7}$

We have,

$2\vec u - \vec v =\vec w$

$⇒(2x+2y-4)\vec a+(-3x+4y+ 2) \vec b=0$

$⇒2x+2y-4=0$ and $-3x+4y+2=0$  [∵ $\vec a,\vec b$ are non-collinear]

$⇒x=10/7, y=4/7$.