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  • Solve the following system of inequalities graphically: 2x + y greater than equal to 6, 3x + 4y les than or equal to 12

Solve the following system of inequalities graphically:

    Q3.    2x +y \geq 6, 3x +4y\leq 12

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2x +y \geq 6, 3x +4y\leq 12

Graphical representation of  2x +y =6\, \, and\, \, 3x +4y=12  is given in the graph below.

For  2x +y \geq 6,

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

 For     3x +4y\leq 12 ,

The  solution to this inequality is region   below the line ( 3x +4y= 12)  including points on this line because points on the line also satisfy the inequality.

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

This can be represented as follows: 

Posted by

seema garhwal

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