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Questions  >>  CBSE XI  >>  Math  >>  Linear Inequalities
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Q)

Solve the following system of inequalities graphically $ x \geq 3, y \geq 2$

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A)
Toolbox:
  • To represent the solution of linear inequality of one or two variable in a plane if the inequality involves $'\geq'$ or $' \leq$ we draw the graph of the line as a thick line to indicate the line is included in the solution set.
  • If the inequality involves $'>'$ as $'<'$ we draw the graph of the line using is not included in the solution set.
  • To solve an inequality $ax+by > c \qquad a \neq 0, b \neq 0 ( or \;> )$
  • We consider the corresponding equation $ax+by =c$ which represents a straight line This line divides the plane into two half planes I and II
  • We take any point in I half plane and check if it satisfies the given inequality will be one half plane (called solution region ) Containing the point satisfying the inequality
Step 1:
For the given inequality $ x \geq 3$ ---------(1)
Consider the equation $x=3$
The graph of the line is shown in the diagram below.
Similarly for the given inequality $ y \geq 2$---------(2)
Consider the equation $y=2$
The graph of this is shown in the diagram below.
Step 2:
For the inequality (1) the line divides the xy plane into two half plane and the region on the right hand side of the line $x=3$ (including the line) is the solution region.
For the inequality (2) the line $y=2$ divides the XY plane into two half plane and the region above the line $y=2$ (including the line y=2) represents the solution region.
Step 3:
Hence the solution of the given system of linear inequalities is represented by the common shaded region, including the points on the lines.
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