SOLUTION: How would you graph the following? 2x+3y <18 3x-y =/< 6 y =/> 0 x=/> 0

Question 1109406: How would you graph the following?
2x+3y <18
3x-y =/< 6
y =/> 0
x=/> 0
Answer by MathLover1(20849) (Show Source): You can put this solution on YOUR website!
1.
to graph the following inequality, first draw the line and decide which side to shade for the required region
Explanation:
Treat the inequality as an equality or as a straight line graph first. Then shade the correct side of the line to indicate the solutions which are less than .
You can use any method to draw the straight line - plot points or use the intercept/gradient method.
I will use the method of the and intercepts.
To find the -intercept, make :

=> -intercept is at (,)
To find the -intercept, make

=> -intercept is at (,)
Now that you have both intercepts you can plot them and draw a solid line through them. This is the line .
You could also write the equation as :

To decide which side of the line to , choose a test point.
(,) is a good one to test:
since given: , you have
=> is

so, (,) is in the required region and the area BELOW the line must be shaded

2. ...do it same way

intercepts:
...set

=> -intercept is at (,)
...set

=> -intercept is at (,)
graph: or

since given solution is a line and all points to the left and above the line

3.
-> here you have graph shaded above -axis including -axis

4.
-> here you have graph shaded starting with -axis including everything to the right

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