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Which system of inequalities is represented by the graph?

Which system of inequalities is represented by the graph?-example-1

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Answer:


\left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.

Explanation:

The diagram shows shaded region which boundary is bounded with two lines.

Equation of the 1st line:

This line passes through the points (-6,0) and (0,-6), so its equation is


(x-(-6))/(0-(-6))=(y-0)/(-6-0)\\ \\(x+6)/(6)=(y)/(-6)\\ \\y=-x-6

Equation of the 2nd line:

This line passes through the points (-2,0) and (0,4), so its equation is


(x-(-2))/(0-(-2))=(y-0)/(4-0)\\ \\(x+2)/(2)=(y)/(4)\\ \\y=2x+4

The origin belongs to the shaded region, so it must satisfy both inequalities, so


-0-6=-6\le 0\Rightarrow correct inequality is
-x-6\le y


2\cdot 0+4=4\ge 0\Rightarrow correct inequality is
2x+4\ge y

Note that signsare with notion "or equal to" because lines are solid.

Answer:


\left\{\begin{array}{l}-x-6\le y\\ \\2x+4\ge y\end{array}\right.\Rightarrow \left\{\begin{array}{l}y\ge -x-6\\ \\ y\le 2x+4\end{array}\right.

User Jonathan Camenisch
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