2. June 2019 RegentsA system of inequalities is graphed on the set of axes below.a) State the system of inequalities represented by the graph.b) State what region A represents.c) State what the entire gray region represents.

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Advanced Engineering Mathematics

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ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

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2. June 2019 Regents
A system of inequalities is graphed on the set of axes below.
a) State the system of inequalities represented by the graph.
b) State what region A represents.
c) State what the entire gray region represents.

Expert Solution

Step 1

Let us say dotted line represent inequality $A$ and other line represents inequality $B .$

First we will find equation of line $A$

Let us take two points from the graph on this line

$(1, 0) a n d (0, 3)$

$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}} = \frac{3 - 0}{0 - 1} = - 3$

$\Rightarrow$ slope $= - 3$

Now, lets find equation using this slope

$(y - y_{1}) = m (x - x_{1}) \Rightarrow y - 0 = - 3 (x - 1) \Rightarrow y = - 3 x + 3$

Now, $y < - 3 x + 3$

because inequality satisfies $(0, 0)$ and line is dotted.

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A system of inequalities is graphed on the set of axes below. A ) State the system of inequalities represented by the graph. ) State what region A represents. =) State what the entire gray region represents.