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Solution of System of Linear Inequalities in Two Variables


Steps involved in working:
  1. There will be two inequalities involving .Draw the lines corresponding to each of the equation.
  2. Shade the region for inequality (1).
    Shade the region for inequality (2).
  3. The double shaded region (for both (1) & (2)) common to both the Inequalities is the required solution region of the system of inequalities.
​Example 1:
Solve graphically:


Solution:
We draw the graphs of the lines

For (1), the points are (0,5) and (4,0).

  1. Region corresponding to includes the region below the line(1) including the points on the line.
  2. Region corresponding to is the region to the right of the line (2) including the line.
  3. Region corresponding to is the region above the line (3).

∴ The common region is the portion ABC.

Example 2:
Solve graphically:


Solution:
The points on the line
  1. are (0,5) and (10,0).
  2. are (0,1) and (1,0).
  3. are (0,0) and (1,1).
  4. is the y-axis and
  5. is the x-axis.

Solution region for
  1. is the region below the line (1).
  2. is the region above the line (2).
  3. is the region above the line (3).
    Note (0, 0) lies on the line. So check some other point, say (0, 2) in the region]
  4. is the region to the right of y-axis.
  5. is the region above the x-axis.
Putting all these regions together, we get the shaded area ABCD in the graph.
[Note:- All lines (boundaries) are included in the region]





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