System of Inequalities

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A single inequality of one or two variables can be solved by plotting the inequality on a coordinate plane and graphing the line. The solution set for an inequality is the entire region which satisfies the given inequation. System of inequalities consist of more than one inequation and in order to find its solution set we should graph all the inequalities on the coordinate plane. After shading the region for each inequality, the common shaded region of all the given inequalities is the solution for the system of inequalities.

Example 1: Solve the given system of inequalities: x + y ≥ -1 and x ≤ 0.

Graph the inequality, x - y ≥ -1 treating it like a general equation.

Similarly graph the inequality x ≤ 0.

Now, shade the region of the given inequalities  
        


according to their signs.

The green line represents x – y ≥ -1.

The red line represents x ≤ 0.

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 ≤ 4, x ≥ 2 and y ≥ 0.

Graph the inequality, x + y ≤ 4 treating it like a general equation.

Similarly graph the inequalities x ≥ 2 and y ≥ 0.


Now, shade the region of the given inequalities    

according to their signs.

The red line represents x + y ≤ 4.

The green line represents x ≥ 2.   
  
The blue line represents y ≥ 0.      
                                                      
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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