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  • Solve the following system of inequalities graphically: x + y less than or equal to 9, y > x, x greater than or equal to 10

Solve the following system of inequalities graphically:

    Q8.    x + y \leq 9, y > x, x\geq 0

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x + y \leq 9, y > x, x\geq 0

Graphical representation of  x+y=9,x=y and  x=0  is given in graph below.

For x + y \leq 9 ,

The  solution to this inequality is region below  line (x+y=9) including points on this line because  points on line also satisfy the inequality.

 For y > x,

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

For x\geq 0, 

The  solution to this inequality is region on right hand side of the line (x=0) 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.

This can be represented as follows: 

Posted by

seema garhwal

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