Question

Solve the following system of inequalities graphically $2x+y\ge 8,x+2y\ge 10$

Answer 1

The set of inequalities are given as,

$2x+y\ge 8$

$x+2y\ge 10$

Simplifying $2x+y\ge 8$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=8$

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

So, the coordinates are $\left(0,8\right)$ and $\left(4,0\right)$.

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

$0\ge 8$

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

Simplifying $x+2y\ge 10$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=5$

When $y=0$, then, $x=10$

So, the coordinates are $\left(0,5\right)$ and $\left(10,0\right)$.

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

$0\ge 10$

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