Determine the coordinate of vertices of the figure formed by a given system of inequalities. f(x){(y>=-4),(y<=2x+2),(2x+y<=6):}

BolkowN 2021-02-15 Answered
Determine the coordinate of vertices of the figure formed by a given system of inequalities.
f(x){y4y2x+22x+y6
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Gennenzip
Answered 2021-02-16 Author has 96 answers

Draw the line y = -4, now to obtain the region located by y4 take any point and substitute in given inequalities y4 if that point satisfies the inequality, then the region represented by that inequality must contain that point. Take (0,0) and 04, the region represented by y 4 is region above the line y=-4
Draw the line y = 2x+2, now to obtain the region located by y2x+2 take any point and substitute in given inequalities y2x+2 if that point satisfies the inequality, then the region represented by that inequality must contain that point. Take (0,0) and 020+202, therefore the region represented by y2x+2 is region lies below line y=2x+2 andmust contain point (0,0)
Draw the line 2x+y = 6, now to obtain the region located by 2x+y 6 take any point and substitute in given inequalities 2x+y6 if that point satisfies the inequality, then the region represented by that inequality must contain that point. Take (0,0) and 20+0606, therefore the region represented by 2x+y6 is region lies below line 2x+y=6 andmust contain point (0,0)
Therefore the graphical representation of given inequalities is shown below: From graph, it is clear that given system of inequalities from a triangle with vertices (1,4), (-3,-4) and (5,-4) R is region enclosed by guve system of inequalities.
image

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