# Graph the following system of inequalities. Show (by shading in) the feasible region. x + 2

Graph the following system of inequalities. Show (by shading in) the feasible region.
$x+2y\le 12$
$2x+y\le 12$
$x\ge 0,y\ge 0$
You can still ask an expert for help

## Want to know more about Inequalities systems and graphs?

• Questions are typically answered in as fast as 30 minutes

Solve your problem for the price of one coffee

• Math expert for every subject
• Pay only if we can solve it

szilincsifs
To graph such an inequality, start by graphing the boundary.
For example, the boundary of $x+2y\le 12$, is the line $x+2y=12$. To graph a line, you only need two points. If x= 0, that equation becomes 2y= 12 so y= 6. Mark (0, 6) on the graph. If y= 0, that equation becomes x= 12 so mark (12, 0) on the graph. Draw the line through those two points.
That line, where x+ 2y= 12, separates $x+2y<12$ from $x+2y>12$. It is easy to see that (0, 0) satisfies $0+2\left(0\right)=0<12$ so every point on the same side of that line as (0, 0) satisfies this inequality. Do the same for each of the other inequalities.
The "feasible region", the region where all of these inequalities are satisfied, is where those all overlap- their "intersection".