Question

Solve the following system of inequalities graphically $x+y\le 9,y>x,x\ge 0$

Answer 1

The set of inequalities are given as,

$x+y\le 9$

$y>x$

$x\ge 0$

Simplifying $x+y\le 9$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=9$

When $y=0$, then, $x=9$

So, the coordinates are $\left(0,9\right)$ and $\left(9,0\right)$.

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

$0\le 9$

Which is true, so the graph will be shaded towards the origin.

Now, when $y>x$, then at $\left(0,0\right)$, $0>0$ will give the false statement, so the graph will be away the origin.