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  • Solve the following system of inequalities graphically: 3x = 2 y less than or equal to 12, x greater than or equal to 1, y greater than or equal to 2

Solve the following system of inequalities graphically:

    Q2.        3x +2y \leq 12,\ x \geq 1, \ y\geq 2

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3x +2y \leq 12,\ x \geq 1, \ y\geq 2

Graphical representation of  x=1 \, \, ,3x+2y=12 and  y=2  is given in graph below.

For x \geq 1 ,

The  solution to this inequality is region on right hand side  of line (x=1) including points on this line because  points on the line also satisfy the inequality.

 For y \geq 2,

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

For 3x+2y\leq 12

The  solution to this inequality is region below  the line (3x+2y= 12) including points on this line because  points on the 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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