Question

Solve the following system of inequalities graphically $2x+y\ge 6,3x+4y\le 12$

Answer 1

The set of inequalities are given as,

$2x+y\ge 6$

$3x+4y\le 12$

Simplifying $2x+y\ge 6$ by substituting different values of $x$ and $y$.

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

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

So, the coordinates are $\left(0,6\right)$ and $\left(3,0\right)$.

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

$0\ge 6$

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

Simplifying $3x+4y\le 12$ by substituting different values of $x$ and $y$.

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

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

So, the coordinates are $\left(0,3\right)$ and $\left(4,0\right)$.

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

$0\le 12$

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