Question

Solve the following system of inequalities graphically.
$2x-y>1,x-2y<-1$

Answer 1

Consider $2x-y>1$................(1)
Draw the graph of $2x-y>1$ by dotted line.
It passes through ($\frac{1}{2}$, 0) [ and (0, -1).
Join these points put x = 0 and y = 0 in (1), we get $0-0>1$ which is false.
$\therefore$ Solution set of (1) is not containing the origin.
Consider $x-2y<-1$................(2)
Draw the graph of $x-2y<-1$ by dotted line.
It passes through (-1, 0) and (-1, 0) and (0, $\frac{1}{2}$)
Join these points, put x = 0 and y = 0 in (2), we get $0-0<-1$ which is false.
$\therefore$ Solution set of (2) is not containing the origin.
Hence, the shaded region represents the solution set of the given system of inequations.