Question

Solve the following system of inequalities graphically $x+y\ge 4,2x-y>12$

Answer 1

The set of inequalities are given as,

$x+y\ge 4$

$2x-y>12$

Simplifying $x+y\ge 4$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=4$

When $y=0$, then, $x=4$

So, the coordinates are $\left(0,4\right)$ and $\left(4,0\right)$.

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

$0\ge 4$

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

Simplifying $2x-y>12$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=-12$

When $y=0$, then, $x=6$

So, the coordinates are $\left(0,-12\right)$ and $\left(6,0\right)$.

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

$0>12$

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