Question

Solve the given inequalities graphically:

$2x+y$ $\ge$ $6$ and $3x+4y$ $\le$ $12$

Answer 1

Given equations are $2x+y\ge 6\Rightarrow y=6-2x$

and $3x+4y\le 12\Rightarrow y=\frac{12-3x}{4}$

Let $f\left(x\right)=6-2x$

and $g\left(x\right)=\frac{12-3x}{4}$

Intersection of this two lines is shown in figure.

Region is shown in the graph.