SOLUTION: The system of inequalities below has exactly N solutions of the form (a, b), where a and b are positive integers. Find the value of N. x+3y is less than or equal to 30 3x+y is le

Algebra ->  Graphs -> SOLUTION: The system of inequalities below has exactly N solutions of the form (a, b), where a and b are positive integers. Find the value of N. x+3y is less than or equal to 30 3x+y is le      Log On


   

Question 935059: The system of inequalities below has exactly N solutions of the form (a, b), where a and b are positive integers. Find the value of N.
x+3y is less than or equal to 30
3x+y is less than or equal to 30
I am sorry I can't put in the "lesser than or equal to" sign, but I hope what I did is understandable. I got 67, but I am probably wrong. Thanks again.
Answer by josgarithmetic(39625) About Me  (Show Source):
You can put this solution on YOUR website!
x+3y<=30 and 3x+y<=30, and then surround each inequality with triple left and triple right curly braces
for rendering purposes.

x%2B3y%3C=30
3y%3C=-x%2B30
y%3C=-x%2F3%2B10


3x%2By%3C=30
y%3C=-3x%2B30

The system can be expressed as system%28y%3C=-x%2F3%2B10%2Cy%3C=-3x%2B30%29

You graph each line and then use the inequality statements to show which region of points
satisfies BOTH statements. (I have not figured out yet how to make the graph properly render
to show this type of graphed system of inequalities.)

This graph is not complete:
graph%28-12%2C12%2C0%2C35%2C-x%2F3%2B10%2C-3x%2B30%29
In fact, the entire graph code rendering is failing, so you probably see nothing there.