Question

Solve the following system of inequalities graphically $2x+y\ge 4,x+y\le 3,2x-3y\le 6$

Answer 1

The set of inequalities are given as,

$2x+y\ge 4$

$x+y\le 3$

$2x-3y\le 6$

Simplifying $2x+y\ge 4$ by substituting different values of $x$ and $y$.

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

When $y=0$, then, $x=2$

So, the coordinates are $\left(0,4\right)$ and $\left(2,0\right)$.

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

$0\ge 4$

Which can never be true, so the graph will be shaded away the origin.

Simplifying $x+y\le 3$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=3$

When $y=0$, then, $x=3$

So, the coordinates are $\left(0,3\right)$ and $\left(3,0\right)$.

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

$0\le 3$

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

Simplifying $2x-3y\le 6$ by substituting different values of $x$ and $y$.

When $x=0$, then, $y=-2$

When $y=0$, then, $x=3$

So, the coordinates are $\left(0,-2\right)$ and $\left(3,0\right)$.

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

$0\le 6$

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