Question

The number of non negative integral solution of the inequation $x+y+z+w\le 7$ is_________

Answer 1

Given inequality

$x+y+z+w\le 7$

If we take x=0,y=1, z=2, w =4.then given equation is satisfied

$0+1+2+4\le 7$

$7=7$

Again put x=1,y=4,z=o, w= 3. Then ,

$\begin{align}

$1+4+0+2\le 7$

$7=7$

If x=-1, y=1, z=3 , w=5 then ,

$-1+1+3+5\le 7$

$8\ne 7$

Which is not possible ,

We can’t take negative value of x,y,z,w

Hence ,

The number of non negative integral solution of the inequation