Question

Need help
answer
showing work​

Answer 1

$\large\underline{\sf{Solution-}}$

Given linear inequality is

$\rm \: x - y \geqslant 8$

Let first represent the above inequality in the form of equation. So, above inequality, in the form of equation is

$\rm \: x - y = 8$

Substituting 'x = 0' in the given equation, we get

$\rm \: 0 - y = 8$

$\rm \: - y = 8$

$\bf\implies \:y \: = \: - \: 8$

Substituting 'y = 0' in the given equation, we get

$\rm \: x - 0 = 8$

$\bf\implies \:x \: = \: 8$

Hᴇɴᴄᴇ,

➢ Pair of points of the given equation are shown in the below table.

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf y \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 0 & \sf - 8 \\ \\ \sf 8 & \sf 0 \end{array}} \\ \end{gathered}$

➢ Now draw a graph using the points (0 , - 8) & (8 , 0)

Now, this line divides the xy - plane in to two parts.

So, To determine the region represented by the inequality x - y $\geqslant$8, we have to apply the (0, 0) test.

So, on substituting (0, 0) in the given inequality, we get

$\rm \: 0 - 0 \geqslant 8$

$\rm \: 0 \geqslant 8$

$\rm\implies \:(0,0) \: doesnot \: satisfy \: the \: given \: inequality.$

➢ See the attachment graph.