SOLUTION: Solving inequalities with two variables I need an example of this and a way to solve it. thank you

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Question 118165: Solving inequalities with two variables

I need an example of this and a way to solve it.
thank you
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

For example, look at the graph of following equality:
2x+%2B3y=6.
Solved by pluggable solver: PLOT a graph of a function
Plotting a graph:
graph%28+600%2C+400%2C+-15%2C+15%2C+-10%2C+15%2C+%28-2%2F3%29x%2B2+%29
This solver uses formula rendering system and here's the actual formula that was plotted:

graph( 600, 400, -15, 15, -10, 15, (-2/3)x+2 )



Recall that when a line is drawn in a plane, the line divides the plane into three sets of points:
two+half-planes and the line+itself.

Now, consider the solution to 2x+%2B3y%3C=6..
Recall that the solution is one of these half-planes along with the+line.
Note that 2x+%2B3y%3C6 would result in the same half-plane;+but+notthe+line.
One method for determining the correct+half-plane is to "test" the inequality with the coordinates of a point that is NOT on the line.
If the coordinates satisfy the inequality, then that+point+and+all+points in that half-plane are solutions.
We then shade+that+half-plane.
Usually the point O=(0,0) is the simplest test+point-provided the line does+not+pass through the+origin.
In this example, the (0,0) satisfies the inequality and gives us the solution:
On graph above, shade the line and the +half-plane which lies on the left from the line.