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  • Solve the following system of inequality graphically: x + 2 y less than or equal to 10, x + y greater than or equal to 1, x - y less than or equal to 0, x greater than or equal to 0, y greater than or equal to 0

Solve the following system of inequality graphically:

    Q15.    x+2y \leq 10, \ x +y \geq 1, \ x-y\leq 0, x\geq 0, \ y\geq 0

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x+2y \leq 10, \ x +y \geq 1, \ x-y\leq 0, x\geq 0, \ y\geq 0

Graphical representation of  x+2y=10 \, \, ,x+y=1\, \, \,,x-y=0\, \, ,x=0\, \, and\, \, y=0  is given in graph below.

For x+2y \leq 10, 

The  solution to this inequality is region below the  line (x+2y=10) including points on this line because  points on line also satisfy the inequality.

 For \ x +y \geq 1,,

The  solution to this inequality is region above the line (x+y=1)  including points on this line because  points on line also satisfy the inequality.

 For \ x-y\leq 0,,

The  solution to this inequality is region above the line (x-y=0)  including points on this line because  points on line also satisfy the inequality.

For \ x \geq 0,

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

For \ y \geq 0,

The  solution to this inequality is region above  the line (y=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 including points on the respective lines.

This can be represented as follows: 

Posted by

seema garhwal

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