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

Solve the inequalities graphically in two - dimensional plane . $3y-5x < 30$

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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 $ax+by > c \qquad a \neq 0, b \neq 0 ( or \;> )$
  • To solve an inequality $ax+by > c \qquad a \neq 0, b \neq 0 ( or \;> )$
The given inequality is $3y-5x < 30$
Consider the equation $3y-5x=30$
We see that the points $(-6,0)$ and $(0,10)$ satisfy the equation.
The graphical representation of the dotted line as shown
Step 2:
The line divides the xy - plane into half planes (0,0) in the half plane II.
we see that $ 3(0) -5(0) <30$
$0 < 30$ is true.
Step 3:
Therefore the half plane I is not the solution region of the inequality.
Thus the solution region of the given inequality is half plane II containing the point (0,0) excluding the line, It is represented by the shaded region.
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