Question

Graph the solution sets of the following inequations :
$$x + y \geq 4$$.

Answer 1

Given $$x+y\ge 4$$

Let us draw the graph of $$x+y=4$$

Put $$x=0\implies 0+y=4\implies y=4$$

$$(0,4)$$ is the solution set of $$x+y=4$$

Put $$y=0\implies x+0=4\implies x=4$$

$$(4,0)$$ is the solution set of $$x+y=4$$

$$\implies (4,0),(0,4)$$ lies on the line $$x+y=4$$

$$(0,0)$$ lies in the left side area of $$x+y=4$$

Let us check that $$(0,0)$$ lies in the area of solution set of $$x+y\ge 4$$

$$x+y=0+0<4$$

$$\implies (0,0)$$ does not lies in the area of solution set of $$x+y\ge 4$$

$$\therefore $$ solution set is the area which right side of $$x+y=4$$