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Graphing the Solution Region of
System of Linear Inequalities in Two Variables:
Example:
Graph the solution set of the system of linear inequalities
Solution:
We have
 ————— (A)
 ————— (B)
The corresponding equations of inequalities (A) and (B)
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 —— (1)
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 —— (2)
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For x – intercept
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For x – intercept
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Put  in (1) we get
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Put  in (2) we get
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For y – intercept
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For y – intercept
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Put  in (1) we get
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Put  in (2) we get
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Test
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Test
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Put origin  in eq (A)
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Put origin  in eq (B)
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 which is true solution set origin side.
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 which is true solution set origin side.
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Example:
Graph the solution set of the system of linear inequalities
Solution:
We have
 ————— (A)
 ————— (B)
The corresponding equations of inequalities (A) and (B)
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 —— (1)
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 —— (2)
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For x – intercept
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For x – intercept
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Put  in (1) we get
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Put  in (2) we get
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For y – intercept
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For y – intercept
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Put  in (1) we get
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Put  in (2) we get
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Test
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Test
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Put origin  in eq (A)
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Put origin  in eq (B)
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 which is true solution set lies origin side.
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 which is true solution set lies origin side.
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Example:
Graph the solution set of the system of linear inequalities
 , 
Solution:
We have
 ————— (A)
 ————— (B)
 ————— (C)
The corresponding equations of inequalities (A) and (B)
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 —— (1)
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 —— (2)
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For x – intercept
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For x – intercept
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Put  in (1) we get
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Put  in (2) we get
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For y – intercept
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For y – intercept
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Put  in (1) we get
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Put  in (2) we get
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Test
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Test
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Put origin  in eq (A)
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Put origin  in eq (B)
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 which is true solution set lies origin side.
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 which is false solution set lies other side of origin.
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Now in inequality (C)  , Solution set right half plane in I and IV Quadrant.
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