How do you graph a system of inequalities? I’m confused about how to find the maximum and minimum values, too!
I would start by treating each inequality as if it were an equation and separately drawing the line for each equation. So let’s say your system of inequalities was
x+y < 8 and x > -4
First, separately graph the line x+y=8 and the line x=-4. Next, look at the inequality symbol, and decide whether your x and y values need to fall above/ below and left/right of the lines you’ve drawn. In my example, your x and y values should fall below and left of the line x+y=8 (because of the < sign), and to the right of the line x = -4 (because our x values should be greater than this line).
Shade in the area where your x and y values satisfy each inequality.
Ex: Area that satisfies x + y < 8 is
and the area that satisfies x > -4 is
To graph the solutions to the system of inequalities, you just need to find where the areas that satisfy the inequalities ALL overlap. This is easy to do visually, especially if you shaded in the other areas in different colors. Here’s the area that satisfies both of the above inequalities:
Once you’ve found the overlapping areas, any point in this area will satisfy all of your inequalities. If you want to find the maximum/minimum x or y value, you can often find it visually by looking for the highest/lowest or leftmost/rightmost point in the overlapping shaded area! In the case I’ve given, we can see that the highest possible y value (y-maximum) is just under y=12.