Graph the following linear inequalities in two variables.

y≤2x-1

Question

03-03-2022
Math

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Graph the following linear inequalities in two variables.

y≤2x-1

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Анонимidn Анонимidn · Answer 1 · 2022-03-06T18:07:15+08:00

[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

[tex]\underline{\mathbb{SOLUTION}:}[/tex]

[tex] \sf \: The \: inequality \: already \: has \: “y” \: on \: the \: left \: so \: no \: need \: to \: rearranged.[/tex]

[tex] \sf \: Plot \: y=2x-1 \: (as \: a \: solid \: line \: because \: “y≤” \: which \: includes \: the \: points \: on \: the \: line \\ \sf \: as \: a \: solution \: of \: the \: inequalities.[/tex]

[tex]\begin{gathered}\begin{gathered} \begin{gathered}\begin{gathered} \begin{gathered}\small\begin{array}{|c|c|c|c|} \hline \\ \ \sf \: \quad \: x\quad&\sf \: \quad 0\quad &\sf \: \quad1\quad&\sf \quad \: 2\quad\\ \hline \\ \sf \green{y}&\sf \green{ - 1}&\sf \green{ 1}&\sf \green{ 3} \\ \hline \\ \sf \: Solutions \sf \: &\sf \: y = 2x - 1 &\sf \: y = 2x - 1&\sf \: y = 2x - 1 \\ \sf \: &\sf \: y = 2(0) - 1&\sf \: y = 2(1) - 1 &\sf \: y =2(2) - 1 \\ \sf \: &\sf \green{y = - 1} &\sf \green{y = 1}&\sf \green{y = 3} \\ \\ \hline \end{array}\end{gathered}\end{gathered}\end{gathered}\end{gathered}\end{gathered} \\ \quad\quad\quad\quad\sf \green{(0,-1)} \quad\quad \quad\quad \sf \green{(1,1)} \quad\quad\quad\quad\sf \green{(2,3)}[/tex]

[tex] \sf \: Shade \: the \: area \: below \: (because \: y \: is \: “y≤") \\ \sf \: The \: shaded \: region \: are \: the \: solutions \: in \: the \: inequality \\ \sf y ≤2x - 1. \: Example \: (2,3), \: (4,1), \: (3,2) \: \\ \sf \: are \: solutions \: because \: they \: are \: located \: in \: the \: \\ \sf \: shaded \: region, \: while \: the \: points \: (-1,3),(-1,5),(0,4) \\ \sf \: are \: not \: solutions.[/tex]

[tex]\color{red}\underline { \huge{\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: }}[/tex]

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