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  • Solve the following system of inequalities graphically: 2x + y greater than or equal to 4, x + y less than 3, 2x - 3y less than or equal to 6

Solve the following system of inequalities graphically:

    Q11.    2x +y \geq 4, \ x + y \leq 3, \ 2x - 3y \leq 6    

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2x +y \geq 4, \ x + y \leq 3, \ 2x - 3y \leq 6

Graphical representation of  2x+y=4 \, \, ,x+y=3 and  2x-3y=6  is given in graph below.

For 2x +y \geq 4, ,

The  solution to this inequality is region above the line (2x+y=4) including points on this line because  points on line also satisfy the inequality.

 For \ x + y \leq 3,,

The  solution to this inequality is region below the line (x+y=3)  including points on this line because  points on line also satisfy the inequality.

For \ 2x - 3y \leq 6,

The  solution to this inequality is region above  the line (2x-3y= 6) including points on this line because  points on line also satisfy the inequality.

 

Hence, solution to these linear inequalities is shaded region as shown in figure including points on the respective lines.

This can be represented as follows: 

Posted by

seema garhwal

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