[tex]\large\underline{\sf{Solution-}}[/tex]
Given linear inequality is
[tex]\rm \: x - y \geqslant 8 \\ [/tex]
Let first represent the above inequality in the form of equation. So, above inequality, in the form of equation is
[tex]\rm \: x - y = 8 \\ [/tex]
Substituting 'x = 0' in the given equation, we get
[tex]\rm \: 0 - y = 8 \\ [/tex]
[tex]\rm \: - y = 8 \\ [/tex]
[tex]\bf\implies \:y \: = \: - \: 8 \\ [/tex]
Substituting 'y = 0' in the given equation, we get
[tex]\rm \: x - 0 = 8 \\ [/tex]
[tex]\bf\implies \:x \: = \: 8 \\ [/tex]
Hᴇɴᴄᴇ,
➢ Pair of points of the given equation are shown in the below table.
[tex]\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}[/tex]
➢ 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 [tex]\geqslant [/tex]8, we have to apply the (0, 0) test.
So, on substituting (0, 0) in the given inequality, we get
[tex] \rm \: 0 - 0 \geqslant 8 \\ [/tex]
[tex] \rm \: 0 \geqslant 8 \\ [/tex]
[tex]\rm\implies \:(0,0) \: doesnot \: satisfy \: the \: given \: inequality. \\ [/tex]
➢ See the attachment graph.
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Answers & Comments
[tex]\large\underline{\sf{Solution-}}[/tex]
Given linear inequality is
[tex]\rm \: x - y \geqslant 8 \\ [/tex]
Let first represent the above inequality in the form of equation. So, above inequality, in the form of equation is
[tex]\rm \: x - y = 8 \\ [/tex]
Substituting 'x = 0' in the given equation, we get
[tex]\rm \: 0 - y = 8 \\ [/tex]
[tex]\rm \: - y = 8 \\ [/tex]
[tex]\bf\implies \:y \: = \: - \: 8 \\ [/tex]
Substituting 'y = 0' in the given equation, we get
[tex]\rm \: x - 0 = 8 \\ [/tex]
[tex]\bf\implies \:x \: = \: 8 \\ [/tex]
Hᴇɴᴄᴇ,
➢ Pair of points of the given equation are shown in the below table.
[tex]\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}[/tex]
➢ 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 [tex]\geqslant [/tex]8, we have to apply the (0, 0) test.
So, on substituting (0, 0) in the given inequality, we get
[tex] \rm \: 0 - 0 \geqslant 8 \\ [/tex]
[tex] \rm \: 0 \geqslant 8 \\ [/tex]
[tex]\rm\implies \:(0,0) \: doesnot \: satisfy \: the \: given \: inequality. \\ [/tex]
➢ See the attachment graph.