# Solution of System of Linear Inequalities in Two Variables

**Steps involved in working:**

- There will be two inequalities involving .Draw the lines corresponding to each of the equation.
- Shade the region for inequality (1).

Shade the region for inequality (2). - The double shaded region (for both (1) & (2)) common to both the Inequalities is the required solution region of the system of inequalities.

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**Example 1:**

Solve graphically:

**Solution:**

We draw the graphs of the lines

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

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

âˆ´ The common region is the portion ABC.

**Example 2:**

Solve graphically:

**Solution:**

The points on the line

- are (0,5) and (10,0).
- are (0,1) and (1,0).
- are (0,0) and (1,1).
- is the y-axis and
- is the x-axis.

**Solution region for**

- is the region below the line (1).
- is the region above the line (2).
- 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] - is the region to the right of y-axis.
- is the region above the x-axis.

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**Note:-**All lines (boundaries) are included in the region]