SOLUTION: Solve the following system of linear inequalities by graphing x+2y £ 3 2x-3y £ 6

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Question 121425: Solve the following system of linear inequalities by graphing
x+2y £ 3
2x-3y £ 6
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
First graph x+2y=3.
x%2B2y=3
2y=3-x
y=%283-x%29%2F2
Slope is -1/2.
Y-intercept is 3/2.
+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+%283-x%29%2F2%29+
Next add 2x-3y=6.
2x-3y=6
-3y=6-2x
y=%282x-6%29%2F3
Slope is 2/3.
Y-intercept is -2.
+graph%28+300%2C+300%2C+-5%2C+5%2C+-10%2C+10%2C+%283-x%29%2F2%2C%282x-6%29%2F3%29+
Looks like they intersect at (3,0).
Check your answer.
x%2B2y=3
%283%29%2B2%280%29=3
3=3
True statement.
2x-3y=6
2%283%29-3%280%29=6
6=6
True statement.
(3,0) satisfies both equations.
It's a good answer.