Question

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

Answer 1

The set of inequalities are given as,

$2x-y>1$

$x-2y<-1$

Simplifying $2x-y>1$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=-1$

When $y=0$, then, $x=0.5$

So, the coordinates are $\left(0,-1\right)$ and $\left(0.5,0\right)$.

Now, if $x=0$ and $y=0$, then,

$0>1$

Which cannot be true, so the graph will be shaded away the origin.

Simplifying $x-2y<-1$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=0.5$

When $y=0$, then, $x=-1$

So, the coordinates are $\left(0,0.5\right)$ and $\left(-1,0\right)$.

Now, if $x=0$ and $y=0$, then,

$0<-1$

Which cannot be true, so the graph will be shaded away the origin.