WME@Kimpton Middle
Twovariable Inequality
Shipping is a very important
element in modern commerce. And a ship will float if
the weight of passengers and crew (x) plus the weight of cargo (y) is less then or equal to the maximum capacity allowable for the ship.
In a middle school, class sizes are limited to 25 students, say.
Let x be the number of girls and
y the number of boys in a class. The total of girls and
boys in a class must not exceed 25.
We have this inequality:
x + y 25 
Each pair of values (x, y) that satisfies
the condition is said to
be a solution of this inequality. One solution is
(14, 11), another is (3, 10), yet another (15, 5).
To better understand inequalities and xy pairs, move your
mouse in the active xy plane below. It will show you the point location
indicated by the mouse. Which way to move to increase x?
decrease x? increase y? decrease y?
Now let's see the solutions to this inequality.
x + y 25 
Move the mouse in the diagram, convince yourself that points
on and to the left of the blue line all satisfy the inequality. And
those to the right do not.
Move the mouse along the blue line. What happens to the sum
x + y?
Ah, but you say, x and y are numbers of people
and they can not be negative or nonintegral.
That is exactly right. With these additional
conditions on the values for x and y, please describe
the points in the xyplane that satisfy these conditions and the
inequality.
