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Q: Solve the following system of inequalities graphically:x + y \geq 4, 2x - y <0

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x + y \geq 4, 2x - y <0

Graphical representation of  x +y =4\, \, and\, \, 2x -y=0  is given in the graph below.

For  x + y \geq 4,

The  solution to this inequality is region above  line (x +y =4)including points on this line because points on the line also satisfy the inequality.

 For  2x - y <0 

The solution to this inequality is half plane corresponding to the line  ( 2x -y=0) containing point (1,0) excluding points on this line because points on the line does not  satisfy the inequality.

Hence, the solution to these linear inequalities is the shaded region as shown in figure including points on line  (x +y =4)  and excluding points on the line( 2x -y=0).

This can be represented as follows: 

 

Posted by

seema garhwal

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