System of linear Inequalities

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A single inequality consisting of a single variable can be solved and the appropriate region consisting of the given inequality is shaded. If more than one inequality consisting of more than one variable is given, then it is known as the system of inequalities. A linear inequation is graphed on the coordinate plane and its appropriate region is shaded to get the solution. Therefore, the system of linear inequalities can be solved when each given inequation is graphed on the coordinate plane and the common region of the inequalities is shaded.

Example 1: Solve the given system of inequalities: x + y ≤ 2 and x – y ≤ 1.

Graph the inequality, x + y ≤ 1 treating it like a general equation.

Similarly graph the inequality x - y ≤ 3.    

Now, shade the region of the given inequalities  

according to their signs.       
 
The red line represents x + y ≤ 2

The green line represents x – y ≤ 1.

The common shaded region is the solution of the given system.

The shaded region continues till the end of the straight lines.

Example 2: Solve the given system of inequalities: x – y ≥ 3 and x + y ≤ 1.

Graph the inequality, x - y ≥ 3 treating it like a general equation.


Similarly graph the inequality x + y ≤ 1

Now, shade the region of the given inequalities
          
according to their signs.

The green line represents x – y ≥ 3.

The red line represents x + y ≤ 1.

The common shaded region is the solution of the given system.

The shaded region continues till the end of the straight lines.


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