Question

The point which does not lie in the half plane $3x-y\le 9$ is

$\left(a\right)(-3,-2)\left(b\right)(1,3)$
$\left(c\right)(3,-1)\left(d\right)(2,3)$

Answer 1

Only point $(3,-1)$ does not satisfies the condition $3x-y\le 9$ i.e., $3\times 3-1\times (-1)=10>9$.
Therefore, answer is $\left(c\right)(3,-1)$

Let's check for other points.

For $(-3,-2),3\times -3-(-2)=-9+2=-7<9$

so, this point will satisfy the given condition $3x-y\le 9$

For $(1,3),3\times 1-3=0<9$

$(1,3)$ will satisfy the given condition $3x-y\le 9$

For point $(2,3),3\times 2-3=3<9$

Point $(2,3)$ will also satisfy the given condition $3x-y\le 9$