Question
Solve the following system of linear inequalities graphically.
- x + y ≥ 5
- x - y $\le$ 3
✓
Answer
Given,
x + y $\geq$ 5..... (1)
x - y $\leq$ 3..... (2)
The graph of linear equation
x + y = 5 is drawn in the figure
We note that the solution of inequality (1) is represented by the shaded region above the line x + y = 5, including the points on the line.
On the same set of axes, we draw the graph of the equation x – y = 3 as shown in the figure. Then we note that inequality (2) represents the shaded region above the line x – y = 3, including the points on the line.
Clearly, the double shaded region, common to the above two shaded regions is the required solution region of the given system of inequalities.
x + y $\geq$ 5..... (1)
x - y $\leq$ 3..... (2)
The graph of linear equation
x + y = 5 is drawn in the figure
We note that the solution of inequality (1) is represented by the shaded region above the line x + y = 5, including the points on the line.
On the same set of axes, we draw the graph of the equation x – y = 3 as shown in the figure. Then we note that inequality (2) represents the shaded region above the line x – y = 3, including the points on the line.
Clearly, the double shaded region, common to the above two shaded regions is the required solution region of the given system of inequalities.
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